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Equivalent Resistance in Parallel Circuit

In case of th...

Question

In case of the circuit shown below, which of the following statements is/are true?

R_{1}, R_{2}

and

R_{3}

are in series.

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R_{2}

and

R_{3}

are in series.

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R_{2}

and

R_{3}

are in parallel

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The equivalent resistance of the circuit is

R_{1} + \frac{R_{2} R_{3}}{R_{2} + R_{3}}

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Solution

The correct options are
C $R_{2}$ and $R_{3}$ are in parallel
D The equivalent resistance of the circuit is $R_{1} + \frac{R_{2} R_{3}}{R_{2} + R_{3}}$
Answer is C and D.
The resistances R2 and R3 are connected to point B which indicates that they are connected in parallel. This statement proves that statements in option A and B are incorrect.
The equivalent resistance of R2 and R3 is given as $\frac{R_{2} R_{3}}{R_{2} + R_{3}}$ as they are connected in parallel.
This equivalent resistance in connected in series with the R1 resistance. So the total resistance in the circuit is given as $R_{1} + \frac{R_{2} R_{3}}{R_{2} + R_{3}}$ .
Hence, the options C and D are correct.

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