Determine the current through the 18-Ω resistor for the circuit shown in the figure assuming that the batteries are ideal.
A)0.25 A
B)0.50 A
C)0.75 A
D)1.0 A

Question

Determine the current through the 18-Ω resistor for the circuit shown in the figure assuming that the batteries are ideal. 
A)0.25 A 
B)0.50 A 
C)0.75 A 
D)1.0 A

Quizplus · Accepted Answer

To solve for the current through the 18-Ω resistor, we need to use Kirchhoff's circuit laws.

First, we apply Kirchhoff's second law (KVL) to the outer loop of the circuit:
- Starting from the top left corner of the diagram, we move clockwise around the outer loop, accounting for the voltage drops across the 12V and 6V batteries and the 24-Ω resistor:
    - 12V - I*R - 6V - I*R - 24I = 0     (where R is the 6-Ω resistor)
- Simplifying and solving for I, we get:
    - I = 0.5 A

This current will divide at the junction between the 24-Ω and 18-Ω resistors according to Kirchhoff's first law (KCL):
- The current going through the 18-Ω resistor will be:
    - I(24Ω) = (0.5 A)(24Ω/(24Ω + 18Ω)) = 0.25 A

Therefore, the current through the 18-Ω resistor is 0.25 A, which corresponds to choice B.

Determine the Current Through the 18-Ω Resistor for the Circuit