Question

THREE RESISTORS RA,RB AND RC ARE CONNECTED IN SERIES AND TO A 120 VOLTS

SOURCE. IF RB = 2 RA, RC = 3RA AND THE TOTAL POWER IS 200 W,

CALCULATE a.) THE RESISTANCE OF EACH RESISTOR

b.) THE POWER IN EACH RESISTOR

Answer 1

The total power:

$$P=\frac {V^2}{R}=\frac{V^2}{R_{A}+R_B+R_C}=\frac{V^2}{R_{A}+2R_A+3R_A},\\\space\\ R_A=\frac{V^2}{6P}=12\Omega,\\\space\\ R_B=2R_A=24\Omega,\\\space\\ R_C=3R_A=36\Omega.$$

The current in the circuit is

$$I=\frac PV=1.67\text A.$$

The power in each resistor:

$$P_A=I^2R_A=33\text W,\\ P_B=I^2R_B=67\text W,\\ P_C=I^2R_C=100\text W.$$