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Question
A set of n identical resistors each of resistance R are connected in series and the effective resistance is found to be X. When these n resistors are connected in parallel the effective resistance is found to be Y find the ratio of X and Y
A set of n identical resistors each of resistance R are connected in series and the effective resistance is found to be X. When these n resistors are connected in parallel the effective resistance is found to be Y find the ratio of X and Y
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Solution
In series connection :
effective resistance of n resistors is given by Rs = R + R + R + R ....... = nR = X .........(1)
In parallel combination :
effective resistance of n resistors is given by 1/Rp = Y = 1/R + 1/R + 1/R + 1/R + ........
Rp = R/n = Y ..........(2)
dividing eq1 by eq. 2, we get :
X/Y = n2
effective resistance of n resistors is given by Rs = R + R + R + R ....... = nR = X .........(1)
In parallel combination :
effective resistance of n resistors is given by 1/Rp = Y = 1/R + 1/R + 1/R + 1/R + ........
Rp = R/n = Y ..........(2)
dividing eq1 by eq. 2, we get :
X/Y = n2
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