Question

An inductive circuit contains resistance of 10 ohms and an inductance of 2H. If an A.C. voltage of 120 volt and frequency 60Hz is applied to this circuit, the current would be nearly
A. 0.16amp
B. 0.3amp
C. 0.48amp
D. 0.8amp

Answer 1

Hint: Here, first we will find out the angular frequency of the circuit using the frequency applied to the circuit. After this, we will use this angular frequency to find the total impedance of the circuit through using the inductance as well as the resistance of the circuit. Then we use the Ohm’s law to obtain the current in the circuit.

Complete step by step answer:
There are two types of materials which bring resistance into the circuit, one is a resistor and another is the inductor. Resistance is the ability of a material to resist the current flowing in the circuit. The frequency applied to the circuit is 60Hz. Thus, the angular frequency of the circuit can be obtained as follows:
\[\omega =2\pi f\]
Here,\[\omega\]is the angular frequency and f is the frequency applied to the circuit. Thus, the angular frequency of the circuit is:
\[
\omega =2\centerdot 3.14\centerdot 60 \\
\Rightarrow \omega =376.8Hz \\
\]
Now, the total impedance of the circuit is given by the below formula;
\[Z=\sqrt{{{(R)}^{2}}+{{(\omega L)}^{2}}}\]
Where, R is the resistance due to the resistor,\[\omega\]is the angular frequency and L is the inductance of the inductor. Thus, the total impedance of the circuit would be as follows:
\[
Z=\sqrt{{{(10)}^{2}}+{{(376.8\centerdot 2)}^{2}}} \\
\Rightarrow Z=735.6\Omega \\
\]
Now, the current produced would be obtained from the Ohm’s law:
\[I=\dfrac{V}{Z}\]
Where I is the current, V is the voltage and Z is the impedance. Thus the current is:
\[I=\dfrac{120}{735.6}\\
\therefore I=0.16\,amp\]

Hence, option A is the correct answer.

Note: In an A.C. circuit, inductance is always ahead the voltage and always lags in the phase difference in the terms for current, while resistance always lagging in terms of phase difference for voltage, while it is always ahead for the phase difference in terms of current, when resistor is compared with the inductor.