In the given circuit, the current in resistance R3 is :
- 1 A
- 1.5 A
- 2 A
- 2.5 A
The Correct Option is A
Approach Solution - 1
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.
Approach Solution -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:
- \(R_2\) and \(R_3\) are in parallel.
- The equivalent resistance of \(R_2\) and \(R_3\) is given by: \(R_{\text{eq}} = \frac{R_2 \cdot R_3}{R_2 + R_3} = \frac{4 \cdot 4}{4 + 4} = 2 \, \Omega\).
- 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.
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