A circuit containing a battery with V = 10.3 V and a resistor R1 = 15.7 $\varOmega$ is shown.If we replace the wire between points a and b with a second resistor R2 = 26.8 $\varOmega$,by how much (in a)will the total current through the battery change?

Question

Quizplus · Accepted Answer

In the original circuit, the total resistance is R1 = 15.7 ohms. Therefore, the total current through the circuit is I1 = V/R1 = 10.3/15.7 = 0.6556 A. 
When the wire between a and b is replaced with R2 = 26.8 ohms, the total resistance becomes R1 + R2 = 15.7 + 26.8 = 42.5 ohms. Therefore, the total current through the circuit is I2 = V/(R1 + R2) = 10.3/42.5 = 0.2424 A. 
The change in current is ΔI = I2 - I1 = 0.2424 - 0.6556 = -0.4132 A ≈ -0.414 A. 
Therefore, the answer is C.

A Circuit Containing a Battery with V = 10 Ω\varOmegaΩ Is ShownIf We Replace the Wire Between Points a and B

A Circuit Containing a Battery with V = 10 $\varOmega$ Is ShownIf We Replace the Wire Between Points a and B