A resistor network consists of and connected in parallel

PHYSICS · Multi-part · A Level · Physics · Electricity · Electricity

Problem

A resistor network consists of

R_1 = 6\,\Omega

and

R_2 = 9\,\Omega

connected in parallel. This parallel combination is then connected in series with

R_3 = 5\,\Omega

and supplied by a variable d.c. source of emf

V

. (a) Derive an expression for the equivalent resistance

R_{\text{eq}}

of the entire network in terms of the given resistor values. (b) Show that the total power

P

dissipated by the network can be written in the form

P = kV^{2}

and determine the numerical value of the constant

k

(with appropriate units). (c) Using the result of part (b), calculate the power dissipated when the supply voltage is (i)

12\,\text{V}

and (ii)

18\,\text{V}

. (d) Find the percentage increase in total power when the voltage is raised from

12\,\text{V}

18\,\text{V}