Answer to Question #276682 in Electric Circuits for Librio

Question

Three resistors R1, R2 and R3 are connected in series-parallel with R1 in series with the parallel combination of R2 and R3. The whole combination is connected across a 120 V DC source. Resistors R1, R2 and R3 take 750 W, 250 W and 200 W respectively. Calculate the resistance R2.

Answer 1

for parallel combination of R2 and R3:

$U_2=U_3$

then:

$U_1+U_2=120$ V

$P_2=U_2I_2=250$ W

$P_3=U_3I_3=200$ W

$I_2/I_3=250/200=1.25$

$I_1=I_2+I_3=2.25I_3$

$P_1/I_1+P_2/I_2=120$

$750/(2.25I_3)+250/(1.25I_3)=120$

$I_3=4.44$ A

$I_2=1.25\cdot4.44=5.56$ A

$U_2=P_2/I_2=250/5.56=44.96$ V

$R_2=U_2/I_2=44.96/5.56=8.09\ \Omega$