Question

Consider the circuit shown in the figure (32-E8). 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,
${\mathrm{R}}_{\mathrm{eff}}=\left(10+20\right)\mathrm{\Omega }=30\mathrm{\Omega }$
The current flowing through the circuit,
$i=\left(\frac{3}{30}\right)\mathrm{A}=0.1\mathrm{A}$

(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,
$R_{\mathrm{eff}}=10\mathrm{\Omega }$
The current flowing through the circuit,
$i=\left(\frac{3}{10}\right)\mathrm{A}=0.3\mathrm{A}$