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 solve for the current in resistance \( R_3 \) in the given circuit, we will follow these steps:

Identify that the resistors \( R_2 \) and \( R_3 \) are in parallel. 

Calculate the equivalent resistance of the parallel combination:

The formula for resistors in parallel is: \(R_{\text{eq}} = \frac{R_2 \times R_3}{R_2 + R_3}\)

Given, \( R_2 = 4 \, \Omega \) and \( R_3 = 4 \, \Omega \).

So, \(R_{\text{eq}} = \frac{4 \times 4}{4 + 4} = 2 \, \Omega\).

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

Total resistance \( R_{\text{total}} = R_1 + R_{\text{eq}} + R_4 = 2 \, \Omega + 2 \, \Omega + 1 \, \Omega = 5 \, \Omega.

Apply Ohm's Law to find the total current in the circuit:

\(I = \frac{V}{R_{\text{total}}}\)

Given voltage \( V = 10 \, V \).

\(I = \frac{10}{5} = 2 \, A\).

This total current \( I \) splits equally between \( R_2 \) and \( R_3 \) because they are identical resistors in parallel.

Therefore, the current through each of \( R_2 \) and \( R_3 \) is:

\(\frac{2}{2} = 1 \, A\).

Hence, the current in resistance \( R_3 \) is 1 A, confirming the correct answer.

Answer 2

To find the current in resistance \( R_3 \), we need to analyze the given circuit using principles of electric circuits.

The circuit is composed of resistors in a combination of series and parallel configurations. We first identify the parts of the circuit that are in series and parallel: 

1. \(R_2\) and \(R_3\) are in parallel.
2. The equivalent resistance of \(R_2\) and \(R_3\) is given by: \(R_{\text{eq}} = \frac{R_2 \cdot R_3}{R_2 + R_3} = \frac{4 \cdot 4}{4 + 4} = 2 \, \Omega\).
3. This equivalent resistor \(R_{\text{eq}}\) is in series with \(R_1\) and \(R_4\).

Calculate the total resistance in the circuit:

\(R_{\text{total}} = R_1 + R_{\text{eq}} + R_4 = 2 \, \Omega + 2 \, \Omega + 1 \, \Omega = 5 \, \Omega\)

Using Ohm’s Law, the total current \(I\) is given by:

\(I = \frac{V}{R_{\text{total}}} = \frac{10}{5} = 2 \, \text{A}\)

The current through the parallel combination of \(R_2\) and \(R_3\) will split. The current \(I_3\) through \(R_3\) is given by the current division rule:

\(I_3 = \frac{R_2}{R_2 + R_3} \cdot I = \frac{4}{4 + 4} \cdot 2 = 1 \, \text{A}\)

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