Physics

Problem

Two resistors,

R

and

3R

, are connected in series to a direct-current source whose potential difference is

V

. a. (i) Derive an expression for the current

I

flowing through the circuit in terms of

V

and

R

. b. (ii) Obtain algebraic expressions for the powers

P_1

and

P_2

dissipated in the resistors

R

and

3R

respectively. c. (iii) Hence find the ratio

P_1 : P_2

. d. (iv) If

V = 12\,\text{V}

and the power in the smaller resistor

R

is required to be

18\,\text{W}

, calculate the numerical value of

R

. (Assume the resistors can safely handle the power involved.)