Two resistors of R Ω and 20 Ω are connected in parallel to get an effective resistance of 15 Ω. Find R.

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Question

This question was previously asked in

RRB ALP Fitter 21 Jan 2019 Official Paper (Shift 2)

Answer 1

CONCEPT:

Resistances in parallel combination: When the terminals of two or more resistances are connected at the same two points and the potential difference across them is equal is called resistances in parallel.

F1 Jitendra Deepak 30.03.2020 D8

The net resistance/equivalent resistance(R) of resistances in parallel is given by:

\(\frac{1}{R} = \frac{1}{{{R_1}}} + \frac{1}{{{R_2}}}\)

CALCULATION:

Given that,

R₁= \(R\ Ω\)

R₂= \(20\ Ω\)

Net resistance/effective resistance (R) = 15 Ω

Use the above-given formula for the parallel combination:

\({{1\over 15}={{1\over R}+{1\over 20}}}\)

\(20R= 300+15R\)

\(5R=300\)

∴\(R=60\ Ω.\)