Physics

Problem

A battery of emf

30\,\text{V}

and negligible internal resistance is connected in series with three resistors

3\,\Omega

7\,\Omega

and

10\,\Omega

. The circuit is kept closed for

5\,\text{min}

. a. (i) Derive a general expression for the energy

W_R

dissipated in a resistor

R

of a series circuit powered by a source of emf

E

for a time

t

. b. (ii) Using your expression, calculate the energy dissipated (in joules) in the

10\,\Omega

resistor during the given time. c. (iii) If the

10\,\Omega

resistor is replaced by a variable resistor

R_x

, obtain an expression for the rate of energy dissipation in

R_x

as a function of

R_x

and determine the value of

R_x

for which this rate is maximum.