Four resistors are connected to a battery with a terminal voltage of 12.0 V, as shown below, with R1 = 45 , R2 = 80 , and R3 = 19 .

Question

(a) Determine the equivalent resistance for the circuit.

(b) Determine the current in the battery.

(c) Determine the current in the 30.0  resistor

(d) Determine the power dissipated by R₁

(e) Determine the power dissipated by R₃

Answer 1

(a) 1/R_1,2 = 1/(30 + 45) + 1/80; R_1,2 = 38.71 Om; R = R_1,2 + R₃ = 38.71 + 19 = 57.71 Om

(b) I = 12.0/57.71 = 0.21 A

(c) I₃ = 0.21 A

(d) P₁ = I₁²·R₁; I₁ = I·R_1,2/(45 + 30) = 0.21·57.71/75 = 0.162 A; P₁ = 0.162²·45 = 1.181 W

(e) P₃ = I₃²·R₃ = 0.21²·19 = 0.838 W