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

To find the current through the 9-Ω resistor, we can use Ohm's Law, which states that V = IR, where V is the voltage, I is the current, and R is the resistance.

First, we can find the equivalent resistance of the circuit using the formula:

Req = R1 + R2 || R3 + R4

where || represents a parallel combination.

Using this formula:

Req = 6 + 4 || 8 + 9 
Req = 6 + 2.3 + 8 
Req = 16.3 Ω

Now we can use Ohm's Law to find the current I:

I = V / Req 
I = 8 / 16.3 
I ≈ 0.49 A

This means that the current through the 9-Ω resistor is closest to 0.7 A (since it is in parallel with the 8-Ω resistor, which has the same voltage drop and thus the same current). Therefore, the best choice is B.

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