Four resistors are connected across an 8-V DC battery as shown in the figure.The current through the 9-Ω resistor is closest to
A)1 A.
B)0.7 A.
C)0.5 A.
D)0.9 A.
E)2 A.

Question

Four resistors are connected across an 8-V DC battery as shown in the figure.The current through the 9-Ω resistor is closest to 
A)1 A. 
B)0.7 A. 
C)0.5 A. 
D)0.9 A. 
E)2 A.

Quizplus · Accepted Answer

Since the resistors are in parallel, the equivalent resistance can be found as
1/R = 1/10 + 1/12 + 1/15 + 1/9
R = 3.202 Ω
Using Ohm's Law, the current through the 9-Ω resistor can be found as
I = V/R = 8 V / 3.202 Ω = 2.495 A 
However, since the 9-Ω resistor is connected in parallel with the 15-Ω resistor, most of the current will flow through the 15-Ω resistor, leaving less current through the 9-Ω resistor. We can estimate the current through the 9-Ω resistor as the total current (8 V / 3.202 Ω = 2.495 A) times the fraction of the total resistance contributed by the 9-Ω resistor (9 Ω / (10 Ω + 12 Ω + 15 Ω + 9 Ω) = 0.225). Therefore, the current through the 9-Ω resistor is approximately 2.495 A x 0.225 = 0.561 A, which is closest to choice B, 0.7 A.

Four Resistors Are Connected Across an 8-V DC Battery as Shown