First slide

combination of resistance

Question

In the circuit given E = 6.0 V, $R_{1} = 100 Ω, R_{2} = R_{3} = 50 Ω, R_{4} = 75 Ω .$ The equivalent resistance of the circuit, in ohms, is

Moderate

A

11.875
B

26.31
C

118.75
D

None of these

Solution

In given circuit three resistance R₂, R₄ and R₃ are parallel.
$\begin{array}{l} \frac{1}{R} = \frac{1}{R_{2}} + \frac{1}{R_{4}} + \frac{1}{R_{3}} \\ = \frac{1}{50} + \frac{1}{50} + \frac{1}{75} \\ = \frac{75 + 75 + 50}{50 \times 75} \end{array}$
$R = \frac{50 \times 75}{75 + 75 + 50} = \frac{50 \times 75}{200} = \frac{75}{4} Ω = 18 .75 Ω$
This resistance is in series with R₁.
$∴ R_{resultant} = R_{1} + R = 100 + 18 .75 = 118 .75 Ω$

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