Four resistors are connected across an ideal dc battery with voltage V as shown in the figure. Assume that all quantities shown are accurate to two significant figures. If the total current through this circuit is I = 2.0 A, what is the current through the 4.0-Ω resistor?
A) 1.0 A
B) 2.0 A
C) 3.0 A
D) 1.3 A
E) 2.4 A

Question

Four resistors are connected across an ideal dc battery with voltage V as shown in the figure. Assume that all quantities shown are accurate to two significant figures. If the total current through this circuit is I = 2.0 A, what is the current through the 4.0-Ω resistor? 
A) 1.0 A 
B) 2.0 A 
C) 3.0 A 
D) 1.3 A 
E) 2.4 A

Quizplus · Accepted Answer

Using Ohm's Law, we can find the voltage drop across the 4.0-Ω resistor. 
V = IR 
V = (2.0 A)(4.0 Ω) 
V = 8.0 V

Next, we can use Kirchhoff's Voltage Law (KVL) to find the voltage drop across the other three resistors combined. 
V = (2.0 Ω)(2.0 A) + (3.0 Ω)(2.0 A) + (6.0 Ω)(2.0 A) 
V = 26 V

Then, we can find the total resistance of the circuit by adding the resistances of all four resistors together. 
R(total) = 2.0 Ω + 3.0 Ω + 4.0 Ω + 6.0 Ω 
R(total) = 15 Ω

Finally, we can use Ohm's Law again to find the current through the 4.0-Ω resistor. 
I = V/R 
I = 8.0 V / 4.0 Ω 
I = 2.0 A

Therefore, the current through the 4.0-Ω resistor is 2.0 A, which is answer choice D.

Four Resistors Are Connected Across an Ideal Dc Battery with Voltage