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Calculate the equivalent resistance between the points A and B in figure if each resistance is 2.0 Ω.

Calculate the equivalent resistance between the points A and B in figure if each resistance is 2.0 Ω. Current Electricity, Concise Physics Solutions ICSE Class 10.

Current Electricity

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Answer

Let the resistors be R1, R2, R3, R4 each of 2.0 Ω.

In parallel, if the equivalent resistance is RP, then

1RP=1R3+1R41RP=12+121RP=22⇒RP=1Ω\dfrac{1}{RP} = \dfrac{1}{R3} + \dfrac{1}{R4} \\[0.5em] \dfrac{1}{RP} = \dfrac{1}{2} + \dfrac{1}{2} \\[0.5em] \dfrac{1}{RP} = \dfrac{2}{2} \\[0.5em] \Rightarrow RP = 1 Ω

Hence, RP = 1 Ω

In series connection,

Equivalent resistance = RE = R1 + R2 + RP
= 2 + 2 + 1 = 5 Ω

Hence, Equivalent resistance = 5 Ω

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