Question

The current flowing through \(R_2\) is

• A. \(\frac{1}{3}A\)
• B. \(\frac{1}{2}A\)
• C. \(\frac{2}{3}A\)
• D. \(\frac{1}{4}A\)

Answer 1

The Correct Option is A

Step 1: Determine the Equivalent Resistance (\( R_{\text{eq}} \))

The total resistance in the circuit is given as:

\[ R_{\text{eq}} = 4 \, \Omega. \]

Step 2: Calculate the Total Current (\( i \))

Using Ohm’s law:

\[ i = \frac{V}{R_{\text{eq}}}. \]

Substitute the given values (\( V = 8 \, \text{V} \), \( R_{\text{eq}} = 4 \, \Omega \)):

\[ i = \frac{8}{4} = 2 \, \text{A}. \]

Step 3: Calculate \( i_1 \)

The current \( i_1 \) is determined using the current division rule:

\[ i_1 = i \cdot \frac{R_2}{R_1 + R_2}, \]

where \( R_1 = 6 \, \Omega \) and \( R_2 = 3 \, \Omega \). Substituting the values:

\[ i_1 = 2 \cdot \frac{3}{3 + 6} = 2 \cdot \frac{3}{9} = \frac{6}{9} = \frac{2}{3} \, \text{A}. \]

Step 4: Calculate \( i_2 \)

The current \( i_2 \) is given by:

\[ i_2 = \frac{i_1}{2}. \]

Substitute \( i_1 = \frac{2}{3} \):

\[ i_2 = \frac{\frac{2}{3}}{2} = \frac{2}{3} \cdot \frac{1}{2} = \frac{1}{3} \, \text{A}. \]

Final Answer:

The calculated currents are:

• \( i = 2 \, \text{A} \)
• \( i_1 = \frac{2}{3} \, \text{A} \)
• \( i_2 = \frac{1}{3} \, \text{A} \)