Question

n resistors each of resistance R are first connected in series and then in a parallel what is the ratio of the total effective resistance of the circuit is series combination and parallel combination






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Answer 1

Answer:

Explanation:

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Answer 2

Given: Number of resistors = n

Resistance of each resistor = RΩ

First, they are connected in series and then in parallel

To Find: Ratio of the total resistance in series to that in parallel

Solution:

In series, the resistance is given as

Rs = R1 + R2 + .. + Rn, where Rs is the effective resistance of the combination

Since all the resistors have the same resistance,

Rs = n x R

Rs = nR                        ..1

In parallel combination, resistance is given as

$\frac{1}{Rp} = \frac{1}{R1} + \frac{1}{R2} .... + \frac{1}{Rn}$

Since all the resistors have the same resistance,

$\frac{1}{Rp} = \frac{n}{R}$

Rp = R / n                   ..2

Rs / Rp = $\frac{nR}{\frac{R}{n} }$

Rs / Rp  = n²

Therefore, the ratio of the effective resistance of the combination in series to the effective resistance in parallel is n².