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In the circuit above, the ammeter reads a current of 5.0 A when R = 8Ω and read...


Question

In the circuit above, the ammeter reads a current of 5.0 A when R = 8Ω and reads 7.0A when R = 5Ω. The value of the unknown resistance X is

Options

A) 10.0Ω

B) 7.5Ω

C) 5.0Ω

D) 2.5Ω


The correct answer is D.

Explanation:

From Ohms Law, E = I(R +X)
=> E = I1(R1 + X)
again, E = I2(R2 + X)
=> I1(R1 + X) = I2(R2 + X)
∴ 5(8 + X) = 7(5 + X)
40 + 5X = 35 + 7X
7X - 5X = 40 - 35
2X = 5
X = 5/2
= 2.5Ω

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Dicussion (1)

  • From Ohms Law, E = I(R +X)
    => E = I1(R1 + X)
    again, E = I2(R2 + X)
    => I1(R1 + X) = I2(R2 + X)
    ∴ 5(8 + X) = 7(5 + X)
    40 + 5X = 35 + 7X
    7X - 5X = 40 - 35
    2X = 5
    X = 5/2
    = 2.5Ω

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