{"id":1578,"date":"2020-12-18T08:42:52","date_gmt":"2020-12-18T03:12:52","guid":{"rendered":"https:\/\/cbselibrary.com\/?p=1578"},"modified":"2020-12-18T16:50:58","modified_gmt":"2020-12-18T11:20:58","slug":"parallel-combination-of-resistance","status":"publish","type":"post","link":"https:\/\/cbselibrary.com\/parallel-combination-of-resistance\/","title":{"rendered":"How do you calculate the total resistance of a parallel circuit?"},"content":{"rendered":"
The Effective Resistance of Resistors Connected in Parallel<\/strong><\/p>\n Important results about parallel combination:<\/strong><\/p>\n People also ask<\/strong><\/p>\n How do you calculate the total resistance of a parallel circuit? The Effective Resistance of Resistors Connected in Parallel There are three important characteristics in a parallel circuit: (a) The potential difference is the same across each resistor. (b) The current that passes through each resistor is inversely proportional to the resistance of the resistor. … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[404],"tags":[4154,4157,4144,452,4138,405,4142,4141,4135,4139,4151,4148,4147,4155,453,454,4149,4150,4146,4145,4153,4143,4156,4152,4134,4140],"yoast_head":"\n\n
\n(a) The potential difference is the same across each resistor.
\n(b) The current that passes through each resistor is inversely proportional to the resistance of the resistor.
\n(c) The total current in the circuit equals to the sum of the currents passing through the resistors in its parallel branches.
\n<\/li>\n
\nWhen such a combination of resistance is connected to a battery, all the resistances have the same potential difference across their ends.<\/li>\n
\nLet, V be the potential difference across the two common points A and B. Then, from Ohm\u2019s law
\nCurrent passing through R1<\/sub>, \u00a0 \u00a0 I1<\/sub> = V\/R1<\/sub> \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 … (i)
\nCurrent passing through R2<\/sub>, \u00a0 \u00a0 I2<\/sub> = V\/R2<\/sub> \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 … (ii)
\nCurrent passing through R3<\/sub>, \u00a0 \u00a0 I3<\/sub> = V\/R3<\/sub> \u00a0 \u00a0 \u00a0 \u00a0 \u00a0… (iii)<\/li>\n
\nI = V\/R \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 … (iv)
\nand I = I1<\/sub> + I2<\/sub> + I3<\/sub>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0… (v)<\/li>\n
\n\\( \\frac{\\text{V}}{\\text{R}}=\\frac{\\text{V}}{{{\\text{R}}_{\\text{1}}}}+\\frac{\\text{V}}{{{\\text{R}}_{\\text{2}}}}+\\frac{\\text{V}}{{{\\text{R}}_{\\text{3}}}}\\text{ }……..\\text{ (vi)} \\)<\/li>\n
\n\\( \\frac{\\text{1}}{\\text{R}}=\\frac{\\text{1}}{{{\\text{R}}_{\\text{1}}}}+\\frac{\\text{1}}{{{\\text{R}}_{2}}}+\\frac{\\text{1}}{{{\\text{R}}_{3}}} \\)<\/strong>
\nThe equivalent resistance of a parallel combination of resistance is less than each of all the individual resistances.<\/li>\n\n
\n
Parallel Circuit Problems with Solutions<\/strong><\/h2>\n
\n
\n
\nCalculate
\n(a) the potential difference across each resistor,
\n(b) the effective resistance, R of the circuit,
\n(c) the current, I, in the circuit,
\n(d) the currents, I1<\/sub>, I2<\/sub>\u00a0and I3<\/sub>\u00a0passing through each resistor.
\nSolution:<\/strong>
\n(a) Since this is a parallel circuit, the potential difference across each resistor is 6 V, same as the potential difference across the battery, which is 6 V.
\n<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"