Question

In the given circuit, the current in resistance R3 is :

• A. 1 A
• B. 1.5 A
• C. 2 A
• D. 2.5 A

Answer 1

The Correct Option is A

To determine the current flowing through resistance \( R_3 \), the following procedure will be executed:

Recognize that resistors \( R_2 \) and \( R_3 \) are connected in parallel.

Compute the combined resistance of the parallel arrangement using the formula: \(R_{\text{eq}} = \frac{R_2 \times R_3}{R_2 + R_3}\)

With \( R_2 = 4 \, \Omega \) and \( R_3 = 4 \, \Omega \), the equivalent resistance is calculated as: \(R_{\text{eq}} = \frac{4 \times 4}{4 + 4} = 2 \, \Omega\).

Next, calculate the total resistance of the circuit. The equivalent parallel resistance \( R_{\text{eq}} \) is in series with \( R_1 \) and \( R_4 \).

The total resistance is \( R_{\text{total}} = R_1 + R_{\text{eq}} + R_4 \). Substituting the given values: \( R_{\text{total}} = 2 \, \Omega + 2 \, \Omega + 1 \, \Omega = 5 \, \Omega.\)

Apply Ohm's Law to ascertain the total current in the circuit: \(I = \frac{V}{R_{\text{total}}}\)

Given the voltage \( V = 10 \, V \), the total current is: \(I = \frac{10}{5} = 2 \, A\).

This total current \( I \) will divide equally between \( R_2 \) and \( R_3 \) due to their identical resistance values in parallel.

Consequently, the current passing through each of \( R_2 \) and \( R_3 \) is: \(\frac{2}{2} = 1 \, A\).

Therefore, the current through resistance \( R_3 \) is 1 A.