Chapter 18, Problem 1CQ

Choose the words that make each statement correct. (i) When two or more resistors are connected in series, the equivalent resistance is always [(a) greater than; (b) less than] any individual resistance. (ii) When two or more resistors are connected in parallel, the equivalent resistance is always [(c) greater than; (d) less than] any individual resistance.

To determine

The equivalent resistance in series circuit.

Answer to Problem 1CQ

Option (a) greater than

Explanation of Solution

The equivalent resistance of two or more resistors in series is,

$R_{eq}=R_1+R_2+\mathrm{.....}+R_n$

The sum of resistances is always greater than the individual resistance.

Conclusion:

When two or more resistors are connected in series, the equivalent resistance is always greater than any individual resistance. Therefore, option (a) is correct.

For the equivalent resistance is always less than any individual resistance, the resistors should be connected in parallel. Therefore, option (b) is incorrect.

To determine

The equivalent resistance in parallel circuit.

Answer to Problem 1CQ

Option (d) less than

Explanation of Solution

The equivalent resistance of two or more resistors in parallel is,

$\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}+\mathrm{.....}+\frac{1}{R_n}$

Conclusion:

When two or more resistors are connected in parallel, the equivalent resistance is always less than any individual resistance. Therefore, option (d) is correct.

For the equivalent resistance is always greater than any individual resistance, the resistors should be connected in series. Therefore, option (c) is incorrect.