Three resistors

PHYSICS · Subjective · CBSE · Physics · Electricity · Electricity

Problem

Three resistors

R_{1}

R_{2}

and

R_{3}

are connected in series to an ideal source of constant emf

V

. The resistor

R_{3}

is replaced by another resistor

R_{3}'

, all other quantities remaining unchanged. (i) Derive an expression for the fractional change in the equivalent resistance,

\displaystyle \frac{R_{s}'-R_{s}}{R_{s}}

, where

R_{s}

and

R_{s}'

are the equivalent resistances before and after replacement. (ii) Show that the fractional change in the circuit current has the same magnitude but opposite sign to that in the equivalent resistance. (iii) Taking

R_{1}=4\,\Omega

R_{2}=6\,\Omega

R_{3}=10\,\Omega

and

R_{3}'=5\,\Omega

, calculate the percentage change in the circuit current. (iv) Comment on how replacing a resistor in a series circuit affects all current-dependent quantities in the circuit.

Related theory

Resistors in Series
Resistor Networks
Combination of resistances
Electricity
Electric Circuits
Ohm's law, V-I graphs and ohmic/non-ohmic conductors
Current Electricity

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