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Concepts Of Physics MCQ Edition [Volume 2]

Exam: Concepts Of Physics MCQ Edition [Volume 2]
Subject: Physics
Chapter: Electric Current in Conductors

Concepts Of Physics MCQ Edition [Volume 2] · Physics · Electric Current in Conductors

A uniform wire with a resistance of 50 ext is cut into 5 equal...

A uniform wire with a resistance of

50 ext{ }\Omega

is cut into

5

equal parts. These parts are subsequently connected in parallel. Determine the equivalent resistance of the combination.

Options

A $250 ext{ }\Omega$
B $6250 ext{ }\Omega$
C $10 ext{ }\Omega$
D $2 ext{ }\Omega$

Correct answer

D. $2 ext{ }\Omega$

Step-by-step solution

The resistance of the uniform wire is

R = 50 \Omega

.

When the wire is cut into

5

equal parts, the resistance of each part becomes

r = \dfrac{R}{5} = \dfrac{50}{5} = 10 \Omega

.

When these

5

parts are connected in parallel, the equivalent resistance

R_{eq}

is given by:

\dfrac{1}{R_{eq}} = \dfrac{1}{r} + \dfrac{1}{r} + \dfrac{1}{r} + \dfrac{1}{r} + \dfrac{1}{r} = \dfrac{5}{r}

R_{eq} = \dfrac{r}{5} = \dfrac{10}{5} = 2 \Omega

.

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