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Physics-

General

Easy

Question

In the circuit given E = 6.0 V, R₁ = 100 ohms, R₂ = R₃ = 50 ohms, R₄ = 75 ohms. The equivalent resistance of the circuit, in ohms, is

11.875
26.31
118.75
None of these

The correct answer is: 118.75

In given circuit three resistance $R subscript 2 end subscript comma R subscript 4 end subscript$ and $R subscript 3 end subscript$ are parallel.

$fraction numerator 1 over denominator R end fraction equals fraction numerator 1 over denominator R subscript 2 end subscript end fraction plus fraction numerator 1 over denominator R subscript 4 end subscript end fraction plus fraction numerator 1 over denominator R subscript 3 end subscript end fraction$
$equals fraction numerator 1 over denominator 50 end fraction plus fraction numerator 1 over denominator 50 end fraction plus fraction numerator 1 over denominator 75 end fraction$
$equals fraction numerator 75 plus 75 plus 50 over denominator 50 cross times 75 end fraction$
$R equals fraction numerator 50 cross times 75 over denominator 75 plus 75 plus 50 end fraction equals fraction numerator 50 cross times 75 over denominator 200 end fraction equals fraction numerator 75 over denominator 4 end fraction capital omega equals 18.75 capital omega$
This resistance is in series with $R subscript 1 end subscript$
\ $R subscript text resultant end text end subscript equals R subscript 1 end subscript plus R equals 100 plus 18.75 equals 118.75 capital omega$

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