Question

The current (I) in the circuit will be : -
 

• A. \(\frac{5}{40}A\)
• B. \(\frac{5}{50}A\)
• C. \(\frac{5}{10}A\)
• D. \(\frac{5}{20}A\)

Answer 1

The Correct Option is B

Let's determine the current \( I \) in the given circuit. The circuit consists of resistors connected in series and parallel, and we need to calculate the total resistance and then use Ohm's Law to find the current.

1. Analyze the circuit: The given circuit can be simplified as follows:
   • There is a 20Ω resistor and a 30Ω resistor in series.
   • This series combination is parallel to another 20Ω resistor.
   • A voltage source of 5V is connected across this parallel combination.
2. Calculate the total resistance of the series part:
   • The series resistance, \( R_{\text{series}} \), is the sum of the resistances: R_{\text{series}} = 20 + 30 = 50 \, \Omega.
3. Calculate the equivalent resistance of the parallel combination:
   • Using the formula for parallel resistors: \frac{1}{R_{\text{total}}} = \frac{1}{R_{\text{parallel}}} + \frac{1}{R_{\text{series}}}
   • Substitute the values: \frac{1}{R_{\text{total}}} = \frac{1}{20} + \frac{1}{50}
   • Solve for \( R_{\text{total}} \): R_{\text{total}} = \frac{1}{\left(\frac{1}{20} + \frac{1}{50}\right)} = \frac{1}{\left(\frac{5}{100} \right)} = \frac{100}{5} = 20 \, \Omega
4. Apply Ohm's Law to find the current \( I \):
   • Ohm's Law is given by: I = \frac{V}{R_{\text{total}}}
   • Substitute the known values: I = \frac{5}{50} = 0.1 \, \text{A}
5. Conclusion:
   • The current \( I \) in the circuit is \frac{5}{50} \, \text{A}, which matches the given correct answer option.