Question

The maximum resistance of a network of five identical resistors of $\frac{1}{5}$ $\Omega$ each can be –

• A. 1 $\Omega$
• B. 0.5 $\Omega$
• C. 0.25 $\Omega$
• D. 0.1 $\Omega$

Answer 1

Answer: (A)

1 $\Omega$

Answer 2

To achieve the maximum resistance, all the resistors should be connected in \textbf{series}. In a series combination:
$R_{\text{total}} = R_1 + R_2 + R_3 + R_4 + R_5.$
Given that each resistor has a resistance of $R = \frac{1}{5} \, \Omega$:
$R_{\text{total}} = \frac{1}{5} + \frac{1}{5} + \frac{1}{5} + \frac{1}{5} + \frac{1}{5}.$
Simplify the addition:
$R_{\text{total}} = \frac{5}{5} = 1 \, \Omega.$
Thus, the maximum resistance of the network is $1 \, \Omega$.