Question

For an $\text{LCR}$ series $\text{AC}$ circuit match the following two columns.
Column-1 Column-2

$\text{(a)}$ If resistance is increased.	$\text{(p)}$ current will increase.
$\text{(b)}$ If capacitance is increased.	$\text{(q)}$ current will decrease.
$\text{(c)}$ If inductance is increased.	$\text{(r)}$ current may increase or decrease.
$\text{(d)}$ If frequency is increased.	$\text{(s)}$ power may increase or decrease.

• A. $\text{(a)}\to \text{(q,s)};\text{(b)}\to \text{(r,s)};\text{(c)}\to \text{(r,s)};\text{(d)}\to \text{(r,s)}$
• B. $\text{(a)}\to \text{(p,s)};\text{(b)}\to \text{(r,s)};\text{(c)}\to \text{(r,s)};\text{(d)}\to \text{(p,s)}$
• C. $\text{(a)}\to \text{(p,r)};\text{(b)}\to \text{(p,s)};\text{(c)}\to \text{(r,s)};\text{(d)}\to \text{(r,s)}$
• D. $\text{(a)}\to \text{(p,s)};\text{(b)}\to \text{(p,s)};\text{(c)}\to \text{(q,s)};\text{(d)}\to \text{(r,s)}$

Answer 1

The correct option is A $\text{(a)}\to \text{(q,s)};\text{(b)}\to \text{(r,s)};\text{(c)}\to \text{(r,s)};\text{(d)}\to \text{(r,s)}$

We know , Power across resistor, $P_{rms}=i_{rms}^{2}R$

When resistance is increased, current is decreased.

But from above formula, power may increase or decrease.

$\therefore \text{(a)}\to \text{(q,s)}$

We know that, $I=\frac{V}{\sqrt{R^2+{(\omega L-\frac{1}{C\omega })}^2}}$

So, increase in the value of capacitance $C$, Inductance $L$ or frequency $\omega$ may or may not increase the current in the circuit.

$\therefore \text{(b)}\to \text{(r,s)};\text{(c)}\to \text{(r,s)};\text{(d)}\to \text{(r,s)}$