Question

The current I drawn from the 5 volt source will be:

• A. 0.17 A
• B. 0.38 A
• C. 0.5 A
• D. 0.67 A

Hint:

When analyzing circuits, always simplify resistances step by step, starting with series and parallel combinations before applying Ohm's law.

Answer 1

The Correct Option is B

In this circuit, we have a combination of resistors. First, we need to find the total resistance in the circuit.
The two resistors, \( 10 \, \Omega \) and \( 20 \, \Omega \), are in series, so the total resistance for this part of the circuit is: \[ R_{\text{series}} = 10 \, \Omega + 20 \, \Omega = 30 \, \Omega \] Now, this combined resistance is in parallel with the \( 10 \, \Omega \) resistor. To find the total resistance of these parallel resistors, we use the formula for parallel resistance: \[ \frac{1}{R_{\text{parallel}}} = \frac{1}{R_{\text{series}}} + \frac{1}{R_{\text{10}}} \] \[ \frac{1}{R_{\text{parallel}}} = \frac{1}{30} + \frac{1}{10} \] \[ \frac{1}{R_{\text{parallel}}} = \frac{1 + 3}{30} = \frac{4}{30} \] \[ R_{\text{parallel}} = \frac{30}{4} = 7.5 \, \Omega \] Now, the total resistance in the circuit is \( R_{\text{parallel}} = 7.5 \, \Omega \). Using Ohm’s Law, the total current \( I \) drawn from the 5 volt source is given by: \[ I = \frac{V}{R} \] \[ I = \frac{5 \, \text{V}}{7.5 \, \Omega} = 0.67 \, \text{A} \] Thus, the current drawn from the source is 0.67 A.