Question

In the given circuit, the current (I) through the battery will be

• A. 1.5A
• B. 2.5A
• C. 1A
• D. 2A

Answer 1

The Correct Option is A

Understanding the Problem

In the given figure, the diodes \( D_1 \) and \( D_3 \) are forward biased and the diode \( D_2 \) is reversed biased. We need to find the current through the battery.

Solution

1. Diode Analysis:

The diodes \( D_1 \) and \( D_3 \) are forward biased, so they act as short circuits (negligible resistance). The diode \( D_2 \) is reverse biased, so it acts as an open circuit (infinite resistance).

2. Equivalent Circuit:

The circuit simplifies to two resistors in parallel: one \( 20 \, \Omega \) resistor and one \( 10 \, \Omega \) resistor. The reverse-biased \( D_2 \) branch is effectively removed from the circuit.

3. Equivalent Resistance (\(R_{eq}\)):

The equivalent resistance of parallel resistors is given by:

\( R_{eq} = \frac{R_1 R_2}{R_1 + R_2} \)

Substituting the values:

\( R_{eq} = \frac{(20)(10)}{(20) + (10)} = \frac{200}{30} = \frac{20}{3} \, \Omega \)

4. Current Through the Battery (I):

Using Ohm's law, \( I = \frac{V}{R} \), where \( V = 10 \, \text{V} \):

\( I = \frac{10}{\frac{20}{3}} = 10 \times \frac{3}{20} = \frac{30}{20} = 1.5 \, \text{A} \)

Final Answer

The current through the battery is \( 1.5 \, \text{A} \).