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ICSE Class 10 Physics Question 12 of 27

Solved Sample Paper 3 — Question 26

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Question 3(iv)

Derive an expression for equivalent resistance in the following case

Derive an expression for equivalent resistance in the this case. Decide, which resistances are in series and parallel. Solve for series and then for parallel. Combine both the results to get the equivalent resistance. Physics Sample Paper Solved ICSE Class 10.

Decide, which resistances are in series and parallel. Solve for series and then for parallel. Combine both the results to get the equivalent resistance.

Answer

In the circuit, there are three parts. In the first part, resistors of R1 and R2 Ω are connected in series. If the equivalent resistance of this part is R's then

R's = R1 + R2

In the second part, resistors of R3 and R4 are connected in series. If the equivalent resistance of this part is R''s then

R''s = R3 + R4

In the third part, the two parts of resistance R's and R''s are connected in parallel. If the equivalent resistance between points A and B is Rp then

1Rp=1Rs′+1Rs′′1Rp=1R1+R2+1R3+R41Rp=R3+R4+R1+R2(R1+R2)(R3+R4)Rp=(R1+R2)(R3+R4)R1+R2+R3+R4\dfrac{1}{R_p} = \dfrac{1}{R'_s} + \dfrac{1}{R''_s} \\[0.5em] \dfrac{1}{R_p} = \dfrac{1}{R_1 + R_2} + \dfrac{1}{R_3 + R_4} \\[0.5em] \dfrac{1}{R_p} = \dfrac{R_3 + R_4 + R_1 + R_2}{(R_1 + R_2)(R_3 + R_4)} \\[0.5em] R_p = \dfrac{(R_1 + R_2)(R_3 + R_4)}{R_1 + R_2 + R_3 + R_4} \\[0.5em]

Hence, equivalent resistance = (R1+R2)(R3+R4)R1+R2+R3+R4\dfrac{(R_1 + R_2)(R_3 + R_4)}{R_1 + R_2 + R_3 + R_4}