Question

For two resistances in combination, parallel connection gives larger effective resistance than the series connection.

• A. True
• B. False

Answer 1

The correct option is B

False

To solve this, take 2 resistors R1 and R2, each of value 1 ohm and 2 ohm respectively.

For parallel circuit,

Equivalent resistance = $\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}$

$\frac{1}{R_{eq}}=\frac{R_1+R_2}{R_1{R}_2}$

$R_{eq}=\frac{R_1{R}_2}{R_1+R_2}$

$R_{eq}=\frac{1\times 2}{1+2}=\frac{2}{3}ohm$

For series circuit,

$R_{eq}$ = $R_1$ + $R_2=1+2=3ohm$

Hence it is clear that equivalent resistance of resistors connected in series is greater than the parallel connection.

So when the resistance of the circuit has to be increased, the resistors are connected in series and when the resistance of the circuit has to be reduced in order to pass heavy current, resistors are connected in parallel. Also, note that the equivalent resistance in parallel combination will be less than even the smallest resistance connected.