Resistors in combination: 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

Resistors in combination: 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 need to first find the total resistance of the circuit.

The 12-Ω and 6-Ω resistors are in series, so their equivalent resistance is:

R1 = 12 Ω + 6 Ω = 18 Ω

The 4-Ω and 9-Ω resistors are in parallel, so their equivalent resistance is:

1/R2 = 1/4 Ω + 1/9 Ω = (9 + 4)/(4*9) Ω 
R2 = 36/13 Ω

Now we can find the total resistance:

RT = R1 + R2 = 18 Ω + 36/13 Ω = 486/13 Ω

The current through the circuit is:

I = V/RT = 8 V / (486/13 Ω) = (8*13)/486 A = 208/243 A

Finally, we can use Ohm's law to find the voltage drop across the 9-Ω resistor:

V = IR = (208/243 A) * (9 Ω) = 1872/243 V

So the current through the 9-Ω resistor is:

I9 = V/R9 = (1872/243 V) / (9 Ω) ≈ 0.7 A

Therefore, the closest answer is B) 0.7 A.

Resistors in Combination: Four Resistors Are Connected Across an 8-V