Question

 Find the current through the 10 Ω resistor when the switch S is open and closed in the given circuit.

Hint:

When the switch is closed, the 30 Ω resistor is bypassed, reducing the total resistance in the circuit.

Answer 1

When the switch S is open, the current flows through the 10 Ω and 30 Ω resistors in series, and the total resistance is: \[ R_{\text{total}} = 10 + 30 = 40 \, \Omega. \] Using Ohm's law: \[ I = \frac{V}{R_{\text{total}}} = \frac{20}{40} = 0.5 \, \text{A}. \] Thus, the current through the 10 Ω resistor when the switch S is open is 0.5 A. When the switch S is closed, the 30 Ω resistor is bypassed, and only the 10 Ω resistor remains in the circuit. The current through the 10 Ω resistor is: \[ I = \frac{V}{R_{\text{total}}} = \frac{20}{10} = 2 \, \text{A}. \] Thus, the current through the 10 Ω resistor when the switch S is closed is 2 A.