Question

Match the following.

Column I		Column II
A	Resistive circuit	1	No power is dissipation
B	Purely inductive or capacitive circuit	2	Maximum power dissipation because of $X_C=X_L$
C	$L-C-R$ series circuit	3	Power dissipated only in the resistor
D	Power dissipated at resonance in $L-C-R$ circuit	4	Maximum power dissipation

• A. A-(1), B-(2), C-(4), D-(3)
• B. A-(4), B-(1), C-(3), D-(2)
• C. A-(3), B-(1), C-(4), D-(2)
• D. A-(2), B-(1), C-(3), D-(4)

Answer 1

Answer: (B)

Case I Resistive circuit If the circuit contains only pure $R$, it is called resistive. In that case $\varphi =0,\cos \varphi =1$.
There is maximum power dissipation.
Case II Purely inductive or capacitive circuit. If the circuit contains only an inductor or capacitor, we know that, the phase difference between voltage and current is $\pi /2$.
Therefore, $\cos \varphi =0$ and no power is dissipated even though a current is flowing in the circuit. This current is sometimes referred to as wattless current.
Case III $L-C-R$ series circuit In an $L-C-R$ series circuit, power dissipated is given by equation $P=I^2\cos \varphi$, where $\varphi ={\tan }^{-1}\left(X_C-X_L\right)/R$
So, $\varphi$ may be non-zero in a $R-L$ or $R-C$ or $L-C-R$ circuit. Even in such cases, power is dissipated only in the resistor.
Case IV Power dissipated at resonance in $L-C-R$ circuit At resonance $X_C=X_L=0$, and $\varphi =0$. Therefore, $\cos \varphi =1$ and $P=I^{2}Z=I^{2}R$. That is maximum power is dissipated in a circuit (through $R$ ) at resononance.