Each resistor in the three circuits in the drawing has the s

Each resistor in the three circuits in the drawing has the same resistance R, and the batteries have the same voltage V. The values for R and V are 9 ? and 6.0 V, respectively. Determine the total power delivered by the battery in each of the three circuits.

Solution

A)

total resistance: R_A = ( 1/(2R) + 1/(2R))^-1    = R

the power is, P_A = V²/R_A   = (6.0) ²  /9 = 4 W

B)

total resistance: R_B = ( 1/(2R) + 1/(2R) + 1/R)^-1    = R/2

the power: P_B=V²/R_B   = (6.0) ²  / (9/2) = 8 W

C)

total resistance: R_C = ( 1/(2R) + 1/(2R))^-1   + R = 2R

power: P_C=V²/R_C   = (6.0) ²  / (2x9) = 2 W