Question

Consider the circuit shown in the figure. Find the current through the 10 Ω resistor when the switch S is (a) open (b) closed.

Answer 1

(a) When S is open, the resistors will be connected in series, as the current will flow through the 20 Ω resistor. The effective resistance,

\[R_{eff}  = \left( 10 + 20 \right)  \Omega = 30  \Omega\]

The current flowing through the circuit,

\[i = \left( \frac{3}{30} \right)  A = 0 . 1  A\]

(b) When S is closed, current will flow through the switch that offers the least resistive path. So, the 20 Ω resistance will be ineffective in this case. The effective resistance in this case,

\[R_{eff}  = 10  \Omega\]

The current flowing through the circuit,

\[i = \left( \frac{3}{10} \right)  A = 0 . 3  A\]