{"id":381,"date":"2025-02-20T19:17:28","date_gmt":"2025-02-20T18:17:28","guid":{"rendered":"https:\/\/knutsson.dk\/wordpress\/?page_id=381"},"modified":"2025-02-26T17:14:19","modified_gmt":"2025-02-26T16:14:19","slug":"resistors-2","status":"publish","type":"page","link":"https:\/\/knutsson.dk\/wordpress\/electronics\/math\/resistors-2\/","title":{"rendered":"Resistors"},"content":{"rendered":"<div class=\"wp-block-post-excerpt\"><p class=\"wp-block-post-excerpt__excerpt\">Calculate voltage, current resistance and power with Ohms law. Formulas for Resistors in series, Resistors in Parallel and Voltage divider <\/p><\/div>\n\n    <div class=\"resistor-calculator\">\r\n        <div class=\"band-row\">\r\n            <label class=\"band-label\">Number&nbsp;of&nbsp;Bands:<\/label>\r\n            <select id=\"bandCount\">\r\n                <option value=\"4\">4 Band<\/option>\r\n                <option value=\"5\">5 Band<\/option>\r\n                <option value=\"6\">6 Band<\/option>\r\n            <\/select>\r\n        <\/div>\r\n\r\n        <div id=\"bandContainer\"><\/div>\r\n\r\n        <button id=\"calculateButton\">Calculate<\/button>\r\n\r\n        <div id=\"result\"><\/div>\r\n    <\/div>\r\n\r\n    <script>\r\n        document.addEventListener(\"DOMContentLoaded\", function() {\r\n            function updateBands() {\r\n                const bandCount = parseInt(document.getElementById('bandCount').value);\r\n                const container = document.getElementById('bandContainer');\r\n                container.innerHTML = '';\r\n\r\n                for (let i = 1; i <= bandCount; i++) {\r\n                    const div = document.createElement('div');\r\n                    div.className = 'band-row';\r\n\r\n                    const label = document.createElement('label');\r\n                    label.className = 'band-label';\r\n                    label.textContent = `Band ${i}:`;\r\n\r\n                    const select = document.createElement('select');\r\n                    select.className = 'band';\r\n                    select.id = `band${i}`;\r\n                    select.onchange = function () {\r\n                        this.style.backgroundColor = this.value;\r\n                        this.style.color = (this.value === 'yellow' || this.value === 'white' || this.value === 'gold' || this.value === 'silver') ? 'black' : 'white';\r\n                    };\r\n\r\n                    let options;\r\n                    if (i <= ((bandCount === 4) ? 2 : 3)) {\r\n                        options = ['black', 'brown', 'red', 'orange', 'yellow', 'green', 'blue', 'violet', 'gray', 'white'];\r\n                    } else if (i === ((bandCount === 4) ? 3 : (bandCount === 5) ? 4 : 4)) {\r\n                        options = ['silver', 'gold', 'black', 'brown', 'red', 'orange', 'yellow', 'green', 'blue', 'violet'];\r\n                    } else if (i === ((bandCount === 4) ? 4 : (bandCount === 5) ? 5 : 5)) {\r\n                        options = ['brown', 'red', 'green', 'blue', 'violet', 'gray', 'gold', 'silver'];\r\n                    } else {\r\n                        options = ['brown', 'red', 'orange', 'yellow', 'blue', 'violet'];\r\n                    }\r\n\r\n                    options.forEach(color => {\r\n                        const opt = document.createElement('option');\r\n                        opt.value = color;\r\n                        opt.textContent = color.charAt(0).toUpperCase() + color.slice(1);\r\n                        opt.style.backgroundColor = color;\r\n                        opt.style.color = (color === 'yellow' || color === 'white' || color === 'gold' || color === 'silver') ? 'black' : 'white';\r\n                        select.appendChild(opt);\r\n                    });\r\n\r\n                    \/\/ Set initial color\r\n                    select.style.backgroundColor = options[0];\r\n                    select.style.color = (options[0] === 'yellow' || options[0] === 'white' || options[0] === 'gold' || options[0] === 'silver') ? 'black' : 'white';\r\n\r\n                    div.appendChild(label);\r\n                    div.appendChild(select);\r\n                    container.appendChild(div);\r\n                }\r\n            }\r\n\r\n            function calculateResistance() {\r\n                const bandCount = parseInt(document.getElementById('bandCount').value);\r\n                let significantDigits = '';\r\n                let multiplier = 1;\r\n                let tolerance = 0;\r\n                let tempCoeff = '';\r\n\r\n                for (let i = 1; i <= bandCount; i++) {\r\n                    const select = document.getElementById(`band${i}`);\r\n                    const color = select.value;\r\n                    \r\n                    if (i <= ((bandCount === 4) ? 2 : 3)) {\r\n                        significantDigits += ['black', 'brown', 'red', 'orange', 'yellow', 'green', 'blue', 'violet', 'gray', 'white'].indexOf(color);\r\n                    } else if (i === ((bandCount === 4) ? 3 : (bandCount === 5) ? 4 : 4)) {\r\n                        multiplier = {'silver': 0.01, 'gold': 0.1, 'black': 1, 'brown': 10, 'red': 100, 'orange': 1000, 'yellow': 10000, 'green': 100000, 'blue': 1000000, 'violet': 10000000}[color];\r\n                    } else if (i === ((bandCount === 4) ? 4 : (bandCount === 5) ? 5 : 5)) {\r\n                        tolerance = {'brown': 1, 'red': 2, 'green': 0.5, 'blue': 0.25, 'violet': 0.1, 'gray': 0.05, 'gold': 5, 'silver': 10}[color];\r\n                    } else {\r\n                        tempCoeff = {'brown': 100, 'red': 50, 'orange': 15, 'yellow': 25, 'blue': 10, 'violet': 5}[color];\r\n                    }\r\n                }\r\n\r\n                const resistance = parseInt(significantDigits) * multiplier;\r\n                let output = `Resistance: ${formatValue(resistance)}\u03a9 \u00b1${tolerance}%`;\r\n                if (bandCount === 6) output += `<br>Temperature Coefficient: ${tempCoeff}ppm\/K`;\r\n\r\n                document.getElementById('result').innerHTML = output;\r\n            }\r\n\r\n            function formatValue(value) {\r\n                if (value >= 1e9) return (value \/ 1e9).toFixed(2) + 'G';\r\n                if (value >= 1e6) return (value \/ 1e6).toFixed(2) + 'M';\r\n                if (value >= 1e3) return (value \/ 1e3).toFixed(2) + 'K';\r\n                return value.toFixed(2);\r\n            }\r\n\r\n            document.getElementById('bandCount').addEventListener('change', updateBands);\r\n            document.getElementById('calculateButton').addEventListener('click', calculateResistance);\r\n\r\n            updateBands(); \/\/ Run on page load\r\n        });\r\n    <\/script>\r\n\r\n    <style>\r\n        .resistor-calculator {\r\n            padding: 20px;\r\n            max-width: 400px;\r\n            margin: 0 auto;\r\n            background: #f5f5f5;\r\n            border-radius: 8px;\r\n        }\r\n        .band-row {\r\n            display: flex;\r\n            align-items: center;\r\n            margin-bottom: 10px;\r\n        }\r\n        .band-label {\r\n            font-weight: bold;\r\n            width: 170px;\r\n            margin-right: 10px;\r\n\t\t\t text-align: right;\r\n        }\r\n        select {\r\n            padding: 5px;\r\n            border: 2px solid #ddd;\r\n            border-radius: 4px;\r\n            cursor: pointer;\r\n            width: 150px;\r\n            transition: all 0.3s ease;\r\n        }\r\n        button {\r\n            padding: 10px 20px;\r\n            background: #0073aa;\r\n            color: white;\r\n            border: none;\r\n            border-radius: 4px;\r\n            cursor: pointer;\r\n            width: 100%;\r\n            margin-top: 15px;\r\n        }\r\n        #result {\r\n            margin-top: 20px;\r\n            padding: 15px;\r\n            background: #fff;\r\n            border-radius: 4px;\r\n            font-weight: bold;\r\n        }\r\n    <\/style>\r\n    \n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n<p><H1>Ohms and Power law<\/H1><\/p>\n<table width=50% >\n<tr>\n<td>\n<p>Voltage(Volt):<\/p>\n<p>$V = I \\cdot R$<\/p>\n<p>$V = \\frac{P}{I}$<\/p>\n<p>$V = \\sqrt{P \\cdot R}$<\/p>\n<\/td>\n<td>\n<p>Current(Ampere):<\/p>\n<p>$I = \\frac{V}{R}$<\/p>\n<p>$I = \\frac{P}{V}$<\/p>\n<p>$I = \\sqrt{\\frac{P}{R}}$<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<p>Resistance(Ohm):<\/p>\n<p>$R = \\frac{V}{I}$<\/p>\n<p>$R = \\frac{V^2}{P}$<\/p>\n<p>$R = \\frac{P}{I^2}$<\/p>\n<\/td>\n<td>\n<p>Power(Watt):<\/p>\n<p>$P = V \\cdot I $<\/p>\n<p>$P = I^2 \\cdot R$ <\/p>\n<p>$P = \\frac{V^2}{R} $<br \/> \n\t\t<\/td>\n<\/tr>\n<\/table>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<h1 class=\"wp-block-heading\">Resistors in series<\/h1>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><p>The total resistance $R_{\\text{total}}$ of resistors in series is the sum of their individual resistances: <\/p>\n<p>$R_{\\text{total}} = R_1 + R_2 + R_3 + \\dots + R_n$<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"alignleft size-large is-resized\"><a href=\"https:\/\/knutsson.dk\/wordpress\/wp-content\/uploads\/2025\/02\/r-series.svg\"><img loading=\"lazy\" decoding=\"async\" width=\"248\" height=\"119\" src=\"https:\/\/knutsson.dk\/wordpress\/wp-content\/uploads\/2025\/02\/r-series.svg\" alt=\"\" class=\"wp-image-478\" style=\"width:416px;height:auto\"\/><\/a><\/figure>\n<\/div><\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<h1 class=\"wp-block-heading\">Resistors in Parallel<\/h1>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><p>The total resistance $R_{\\text{total}}$ of resistors in parallel is the reciprocal of the sum of their reciprocals:<\/p>\n<p>$R_{\\text{total}} = \\frac{1}{\\frac{1}{R_1} + \\frac{1}{R_2} + \\frac{1}{R_3} + \\dots + \\frac{1}{R_n}}$<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"alignleft size-large is-resized\"><a href=\"https:\/\/knutsson.dk\/wordpress\/wp-content\/uploads\/2025\/02\/r-parallel.svg\"><img loading=\"lazy\" decoding=\"async\" width=\"203\" height=\"97\" src=\"https:\/\/knutsson.dk\/wordpress\/wp-content\/uploads\/2025\/02\/r-parallel.svg\" alt=\"\" class=\"wp-image-477\" style=\"width:416px;height:auto\"\/><\/a><\/figure>\n<\/div><\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<h1 class=\"wp-block-heading\">Voltage divider<\/h1>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><p>The output voltage $V_{\\text{out}}$ of a voltage divider with two resistors $R_1$ and $R_2$ is:<\/p>\n<p>$V_{\\text{out}} = V_{\\text{in}} \\cdot \\frac{R_2}{R_1 + R_2}$<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"alignleft size-large is-resized\"><a href=\"https:\/\/knutsson.dk\/wordpress\/wp-content\/uploads\/2025\/02\/v-div.svg\"><img loading=\"lazy\" decoding=\"async\" width=\"162\" height=\"164\" src=\"https:\/\/knutsson.dk\/wordpress\/wp-content\/uploads\/2025\/02\/v-div.svg\" alt=\"\" class=\"wp-image-479\" style=\"width:205px;height:auto\"\/><\/a><\/figure>\n<\/div><\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<h2 class=\"wp-block-heading\">Resistors math example<\/h2>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n\n   <h3>Values:<\/h3>\n    <ul>\n        <li>\\( R_1 = 100\\,\\Omega \\), \\( R_2 = 220\\,\\Omega \\) (in series)<\/li>\n        <li>\\( R_3 = 470\\,\\Omega \\) (in parallel with \\( R_1 + R_2 \\))<\/li>\n        <li>Supply Voltage \\( U = 5\\,\\text{V} \\)<\/li>\n    <\/ul><br>\n<div class=\"mymj\">\n   <h3>Total resistance (\\( R_{\\text{total}} \\)):<\/h3>\n    <p>$ R_{\\text{series}} = R_1 + R_2 $<\/p>\n    <p>$ = 100\\,\\Omega + 220\\,\\Omega $<\/p>\n    <p class=\"su\">$ = 320\\,\\Omega $<\/p>\n    <br>\n    <p>$ \\frac{1}{R_{\\text{total}}} = \\frac{1}{R_{\\text{series}}} + \\frac{1}{R_3} $<\/p>\n    <p>$ = \\frac{1}{320} + \\frac{1}{470} $<\/p>\n    <p>$ \\approx 0.00525266 $<\/p>\n    \n    <p>$ R_{\\text{total}} = \\frac{1}{0.00525266} $<\/p>\n    <p class=\"uu\">$ \\approx 190.38\\,\\Omega $<\/p>\n\n\n    <h3>Total current (\\( I_{\\text{total}} \\)):<h3>\n    <p>$ I_{\\text{total}} = \\frac{U}{R_{\\text{total}}} $<\/p>\n    <p>$ = \\frac{5\\,\\text{V}}{190.38\\,\\Omega} $<\/p>\n    <p>$ \\approx 0.02626\\,\\text{A} $<\/p>\n    <p class=\"uu\">$ = 26.26\\,\\text{mA} $<\/p>\n\n    <h3>Voltage drops:<\/h3>\n    <ul>\n        <li>Across \\( R_1 \\) and \\( R_2 \\):\n            <p>$ U_{\\text{series}} = 5\\,\\text{V} $<\/p>\n            <p>$ U_1 = \\frac{R_1}{R_{\\text{series}}} \\cdot U_{\\text{series}} $<\/p>\n            <p>$ = \\frac{100}{320} \\cdot 5\\,\\text{V} $<\/p>\n            <p class=\"uu\">$ \\approx 1.56\\,\\text{V} $<\/p><br>\n            \n            <p>$ U_2 = \\frac{R_2}{R_{\\text{series}}} \\cdot U_{\\text{series}} $<\/p>\n            <p>$ = \\frac{220}{320} \\cdot 5\\,\\text{V} $<\/p>\n           <p class=\"uu\">$ \\approx 3.44\\,\\text{V} $<\/p><br>\n        <\/li>\n        <li>Across \\( R_3 \\):\n            <p class=\"uu\">$ U_3 = 5\\,\\text{V} $<\/p><br>\n        <\/li>\n    <\/ul>\n\n    <h3>Current through each resistor:<\/h3>\n    <ul>\n        <li>Through \\( R_1 \\) and \\( R_2 \\):\n            <p>$ I_{\\text{series}} = \\frac{U_{\\text{series}}}{R_{\\text{series}}} $<\/p>\n            <p>$ = \\frac{5\\,\\text{V}}{320\\,\\Omega} $<\/p>\n            <p class=\"uu\">$ \\approx 15.63\\,\\text{mA} $<\/p><br>\n        <\/li>\n        <li>Through \\( R_3 \\):\n            <p>$ I_3 = \\frac{U_3}{R_3} $<\/p>\n            <p>$ = \\frac{5\\,\\text{V}}{470\\,\\Omega} $<\/p>\n            <p class=\"uu\">$ \\approx 10.64\\,\\text{mA} $<\/p><br>\n        <\/li>\n    <\/ul>\n\n    <h3>Power dissipation:<\/h3>\n    <ul>\n        <li>Power in \\( R_1 \\):\n            <p>$ P_1 = I_{\\text{series}}^2 \\cdot R_1 $<\/p>\n            <p>$ = (0.01563\\,\\text{A})^2 \\cdot 100\\,\\Omega $<\/p>\n            <p class=\"uu\">$ \\approx 24.41\\,\\text{mW} $<\/p><br>\n        <\/li>\n        <li>Power in \\( R_2 \\):\n            <p>$ P_2 = I_{\\text{series}}^2 \\cdot R_2 $<\/p>\n            <p>$ = (0.01563\\,\\text{A})^2 \\cdot 220\\,\\Omega $<\/p>\n            <p class=\"uu\">$ \\approx 53.71\\,\\text{mW} $<\/p><br>\n        <\/li>\n        <li>Power in \\( R_3 \\):\n            <p>$ P_3 = \\frac{(U_3)^2}{R_3} $<\/p>\n            <p>$ = \\frac{(5\\,\\text{V})^2}{470\\,\\Omega} $<\/p>\n            <p class=\"uu\">$ \\approx 53.19\\,\\text{mW} $<\/p>\n        <\/li>\n    <\/ul>\n\n   <h3>Total power dissipation (\\( P_{\\text{total}} \\)):<\/h3>\n    <p>$ P_{\\text{total}} = U \\cdot I_{\\text{total}} $<\/p>\n    <p>$ = 5\\,\\text{V} \\cdot 0.02626\\,\\text{A} $<\/p>\n    <p class=\"uu\">$ \\approx 131.3\\,\\text{mW} $<\/p>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large is-resized\"><a href=\"https:\/\/knutsson.dk\/wordpress\/wp-content\/uploads\/2025\/02\/r-example.svg\"><img loading=\"lazy\" decoding=\"async\" width=\"259\" height=\"204\" src=\"https:\/\/knutsson.dk\/wordpress\/wp-content\/uploads\/2025\/02\/r-example.svg\" alt=\"\" class=\"wp-image-698\" style=\"width:416px;height:auto\"\/><\/a><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Calculate voltage, current resistance and power with Ohms law. Formulas for Resistors in series, Resistors in Parallel and Voltage divider<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":385,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"_s2mail":"yes","ngg_post_thumbnail":0,"footnotes":""},"class_list":["post-381","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/knutsson.dk\/wordpress\/wp-json\/wp\/v2\/pages\/381","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/knutsson.dk\/wordpress\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/knutsson.dk\/wordpress\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/knutsson.dk\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/knutsson.dk\/wordpress\/wp-json\/wp\/v2\/comments?post=381"}],"version-history":[{"count":158,"href":"https:\/\/knutsson.dk\/wordpress\/wp-json\/wp\/v2\/pages\/381\/revisions"}],"predecessor-version":[{"id":763,"href":"https:\/\/knutsson.dk\/wordpress\/wp-json\/wp\/v2\/pages\/381\/revisions\/763"}],"up":[{"embeddable":true,"href":"https:\/\/knutsson.dk\/wordpress\/wp-json\/wp\/v2\/pages\/385"}],"wp:attachment":[{"href":"https:\/\/knutsson.dk\/wordpress\/wp-json\/wp\/v2\/media?parent=381"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}