A 30 resistor is connected in parallel with a 60 Q resistor

A 30 resistor is connected in parallel with a 6.0 Q resistor. This combination is connected in series with a 4.00 resistor. The resistons are connected to a 12. volt battery. How much power is dissipated in the 3.0 resistor? A) 7.7 W E) 5.3 W DO 12 W B) 2.7 W C) 6 W

Solution

3 ohms and 6 ohms are in parallel ,so

1/R₁ =1/3 + 1/6

R₁=2 ohms

2 ohms and 4 ohms are in series ,so equivalent resistance

R_eq=2+4 =6 ohms

Total current flowing in the circuit

I=V/R_eq =12/6 =2 A

Voltage across 4 ohms

V₄=IR₄ =2*4 =8 Volts

Voltage across 3 and 6 ohms is

V₃=V₆=V-V₄=12-8 =4 volts

so power dissipated in 3 ohms resistor is

P₃=V₃²/R₃ =4²/3

P₃=5.3 W