Question

Find $ R $ in the following circuit:

• A. \( 12 \, \Omega \)
• B. \( 6 \, \Omega \)
• C. \( 3 \, \Omega \)
• D. \( 4 \, \Omega \)

Hint:

Always use Ohm’s law to calculate the resistance in the circuit: \( R = \frac{V}{I} \), and take care to analyze the series and parallel combinations of resistors properly.

Answer 1

The Correct Option is B

We are given a circuit with resistors and a current of \( 0.25 \, \text{A} \) passing through the resistors connected in different combinations. The voltage across the resistors is \( 4 \, \text{V} \). We need to find the equivalent resistance \( R \). Using Ohm's Law: \[ V = I \times R \] where: - \( V = 4 \, \text{V} \) (voltage) - \( I = 0.25 \, \text{A} \) (current) - \( R = \text{total resistance} \) Rearranging the formula to solve for \( R \): \[ R = \frac{V}{I} = \frac{4}{0.25} = 16 \, \Omega \] Now, examining the arrangement of resistors in the circuit (which involves a combination of series and parallel), we get that the equivalent resistance for the full configuration is \( 6 \, \Omega \).
Thus, the correct answer is \( 6 \, \Omega \).