{"id":3113,"date":"2024-08-26T20:55:23","date_gmt":"2024-08-26T20:55:23","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=3113"},"modified":"2024-08-26T20:55:24","modified_gmt":"2024-08-26T20:55:24","slug":"series-circuits","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/08\/26\/series-circuits\/","title":{"rendered":"\u00a0Series Circuits"},"content":{"rendered":"\n

 shows three resistors R<\/em>1<\/sub>, R<\/em>2<\/sub> and R<\/em>3<\/sub> connected end to end, i.e., in series, with a battery source of V<\/em> volts. Since the circuit is closed, a current I<\/em> will flow and the voltage across each resistor may be determined from the voltmeter readings V<\/em>1<\/sub>, V<\/em>2<\/sub> and V<\/em>3<\/sub>.<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Figure 3.1<\/strong> : Series circuit<\/p>\n\n\n\n

In a series circuit:<\/p>\n\n\n\n

(a) <\/a>the current I<\/em> is the same in all parts of the circuit; therefore, the same reading is found on each of the two ammeters shown, and,<\/p>\n\n\n\n

(b) <\/a>the sum of the voltages V<\/em>1<\/sub>, V<\/em>2<\/sub> and V<\/em>3<\/sub> is equal to the total applied voltage, V<\/em>, i.e.,<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

From Ohm\u2019s law:<\/p>\n\n\n\n

V<\/em>1<\/sub> =IR<\/em>1<\/sub>, V<\/em>2<\/sub> =IR<\/em>2<\/sub>, V<\/em>3<\/sub> =IR<\/em>3<\/sub> and V<\/em> =IR<\/em><\/p>\n\n\n\n

where R<\/em> is the total circuit resistance.<\/p>\n\n\n\n

Since V<\/em> =V<\/em>1<\/sub> +V<\/em>2<\/sub> +V<\/em>3<\/sub><\/p>\n\n\n\n

then IR<\/em> =IR<\/em>1<\/sub> +IR<\/em>2<\/sub> +IR<\/em>3<\/sub><\/p>\n\n\n\n

Dividing throughout by I<\/em> gives:<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

So, for a series circuit, the total resistance is obtained by adding together the values of the separate resistances.<\/p>\n\n\n\n

Example 3.1<\/h5>\n\n\n\n

For the circuit shown in\u00a0Figure 3.2, determine (a) the battery voltage\u00a0V<\/em>, (b) the total resistance of the circuit, and (c) the values of resistance of resistors\u00a0R<\/em>1<\/sub>,\u00a0R<\/em>2<\/sub>\u00a0and\u00a0R<\/em>3<\/sub>, given that the voltages across\u00a0R<\/em>1<\/sub>,\u00a0R<\/em>2<\/sub>\u00a0and\u00a0R<\/em>3<\/sub>\u00a0are 5\u00a0V, 2\u00a0V and 6\u00a0V, respectively.<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Figure 3.2<\/strong>\u00a0: Circuit for\u00a0Example 3.1<\/p>\n\n\n\n

Solution<\/h5>\n\n\n\n

(a) <\/a>Battery voltage V<\/em>=V<\/em>1<\/sub>+V<\/em>2<\/sub>+V<\/em>3<\/sub><\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

(b) <\/a>Total circuit resistance \"image\"<\/a><\/p>\n\n\n\n

(c) <\/a>Resistance \"image\"<\/p>\n\n\n\n

Resistance \"image\"<\/p>\n\n\n\n

Resistance \"image\"<\/p>\n\n\n\n

(Check: R<\/em>1<\/sub> +R<\/em>2<\/sub> +R<\/em>3<\/sub> = 1.25 + 0.5 + 1.5 = 3.25 \u03a9 =R<\/em>)<\/p>\n\n\n\n

Example 3.2<\/h5>\n\n\n\n

For the circuit shown in\u00a0Figure 3.3, determine the voltage across resistor\u00a0R<\/em>3<\/sub>. If the total resistance of the circuit is 100 \u03a9, determine the current flowing through resistor\u00a0R<\/em>1<\/sub>. Find also the value of resistor\u00a0R<\/em>2<\/sub>.<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Figure 3.3<\/strong>\u00a0: Circuit for\u00a0Example 3.2<\/p>\n\n\n\n

Solution<\/h5>\n\n\n\n

Voltage across R<\/em>3<\/sub>, V<\/em>3<\/sub> = 25-10-4=11<\/strong> V<\/strong><\/p>\n\n\n\n

Current \"image\" which is the current flowing in each resistor<\/p>\n\n\n\n

Resistance \"image\"<\/p>\n\n\n\n

Example 3.3<\/h5>\n\n\n\n

A 12 V battery is connected in a circuit having three series-connected resistors having resistances of 4 \u03a9, 9 \u03a9 and 11 \u03a9. Determine the current flowing through, and the voltage across the 9 \u03a9 resistor. Find also the power dissipated in the 11 \u03a9 resistor.<\/a><\/p>\n\n\n\n

Solution<\/h5>\n\n\n\n

The circuit diagram is shown in\u00a0Figure 3.4.<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Figure 3.4<\/strong>\u00a0: Circuit for\u00a0Example 3.3<\/p>\n\n\n\n

Total resistance R<\/em>=4+9+11=24 \u03a9<\/p>\n\n\n\n

Current \"image\" which is the current in the 9 \u03a9 resistor.<\/p>\n\n\n\n

Voltage across the 9 \u03a9 resistor, \"image\"<\/p>\n\n\n\n

Power dissipated in the 11 \u03a9 resistor,<\/p>\n\n\n\n

\"image\"\/<\/figure>\n","protected":false},"excerpt":{"rendered":"

 shows three resistors R1, R2 and R3 connected end to end, i.e., in series, with a battery source of V volts. Since the circuit is closed, a current I will flow and the voltage across each resistor may be determined from the voltmeter readings V1, V2 and V3. Figure 3.1 : Series circuit In a series circuit: (a) the current I is the same in all parts of the circuit; therefore, the […]<\/p>\n","protected":false},"author":1,"featured_media":3114,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[426],"tags":[],"class_list":["post-3113","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-series-and-parallel-networks"],"jetpack_featured_media_url":"https:\/\/workhouse.sweetdishy.com\/wp-content\/uploads\/2024\/08\/images-2-2.png","_links":{"self":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/3113","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/comments?post=3113"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/3113\/revisions"}],"predecessor-version":[{"id":3115,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/3113\/revisions\/3115"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media\/3114"}],"wp:attachment":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media?parent=3113"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=3113"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=3113"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}