{"id":1571,"date":"2023-04-17T10:00:14","date_gmt":"2023-04-17T04:30:14","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=1571"},"modified":"2023-04-18T10:04:52","modified_gmt":"2023-04-18T04:34:52","slug":"series-combination-of-resistance","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/series-combination-of-resistance\/","title":{"rendered":"How do you calculate the total resistance of a series circuit?"},"content":{"rendered":"
The Effective Resistance of Resistors Connected in\u00a0Series<\/strong><\/p>\n Some results about series combination:<\/strong><\/p>\n People also ask<\/strong><\/p>\n <\/p>\n","protected":false},"excerpt":{"rendered":" How do you calculate the total resistance of a series circuit? The Effective Resistance of Resistors Connected in\u00a0Series There are three important characteristics in a series circuit: (a) The current passing through each resistor is the same. (b) The potential difference across each resistor depends directly on its resistance. (c) The sum of the potential […]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[404],"tags":[4154,4157,4144,451,4138,405,4142,4141,4136,4139,4151,4148,4147,4155,4149,4150,4146,4145,4153,4143,449,450,4156,4152,4137,4140],"yoast_head":"\n\n
\n(a) The current passing through each resistor is the same.
\n(b) The potential difference across each resistor depends directly on its resistance.
\n(c) The sum of the potential difference across each resistor is equal to the total potential difference of the source.
\n<\/li>\n
\nWhen a series combination of resistances is connected to a battery, the same current (I) flows through each of them.<\/li>\n
\nR = R1<\/sub> + R2<\/sub>\u00a0+ R3<\/sub> + … \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0…. (i)<\/li>\n
\nLet, R1<\/sub>, R2\u00a0<\/sub>and R3<\/sub>\u00a0be the resistances connected in series, I be the current flowing through the circuit, i.e., passing through each resistance, and V1<\/sub>, V2\u00a0<\/sub>and V3<\/sub>\u00a0be the potential difference across R1<\/sub>, R2\u00a0<\/sub>and R3<\/sub> respectively. Then, from Ohm\u2019s law,
\nV1<\/sub> = IR1<\/sub>, V2<\/sub> = IR2<\/sub> and V3<\/sub> = IR3<\/sub>\u00a0 \u00a0 \u00a0 … (ii)<\/li>\n
\nV = V1<\/sub> + V2<\/sub> + V3<\/sub>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0… (iii)<\/li>\n
\nV = IR \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 … (iv)<\/li>\n
\nIR = V = V1<\/sub> + V2<\/sub> + V3<\/sub>
\nIR =\u00a0IR1<\/sub> + IR2<\/sub>\u00a0+ IR3
\n<\/sub>IR = I (R1<\/sub> + R2<\/sub>\u00a0+ R3<\/sub> )
\nR = R1<\/sub> + R2<\/sub>\u00a0+ R<\/strong>3<\/strong>
\n<\/sub>Therefore, when resistances are combined in series, the equivalent resistance is higher than each individual resistance.<\/li>\n
\n<\/li>\n<\/ol>\n\n
\n(i.e. voltage of the battery in the circuit), is equal to the sum of the voltage drop
\n(or potential difference) across each individual resistor.<\/li>\n<\/ol>\n\n
Series Circuit Problems with Solutions<\/strong><\/h2>\n
\n
\n
\nCalculate
\n(a) the effective resistance, R of the circuit,
\n(b) the current, I in the circuit,
\n(c) the potential differences across each resistor, V1<\/sub>, V2\u00a0<\/sub>and V3<\/sub>.
\nSolution:
\n<\/strong>
\nNote that the larger the resistance, the larger the potential difference across it. The sum of the potential difference across each resistor is the same as the potential difference across the battery.<\/li>\n<\/ol>\n