Question

derive the expression for equivalent resistance when five resistance connected is parallel combination
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Answer 1

Answer:

$\frac{1}{r \: equivalent} = \frac{1}{r1} + \frac{1}{r2} + \frac{1}{r3} + \frac{1}{r4} + \frac{1}{r5} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Answer 2

Answer:

Consider four resistors of resistances R1, R2, R3 and R4 are connected in parallel as shown in Fig. A source of emf V is connected to the parallel combination. When resistors are in parallel, the potential difference (V) across each resistor is the same. A current I entering the combination gets divided into I1, I2, I3 and I4 through R1, R2, R3 and R4 respectively, such that I = I1 + I2 + I3 + I4.

By Ohm’s law where RP is the equivalent or effective resistance of the parallel combination. Thus, when a number of resistors are connected in parallel, the sum of the reciprocal of the resistance of the individual resistors is equal to the reciprocal of the effective resistance of the combination. If two resistors R1 & R2 are connected in parallel, then Rp = R1R2/(R1 + R2) If three resistors R1, R2 & R3 are connected in parallel, then Rp = R1R2 R3 /(R1R2 + R2R3 + R3R1)Read more on Sarthaks.com - https://www.sarthaks.com/425240/derive-expression-for-equivalent-resistance-when-the-resistors-are-connected-parallel

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