Question

An electric motor that is loaded has an effective resistance of $30\Omega$ and an inductive reactance of $40\Omega$. If the motor is powered by a source with a maximum voltage of $420V$, the maximum current is?
A. 6A
B. 8.4A
C. 10A
D. 12A
E. 13A

Answer 1

You could recall the expression for impedance for a circuit containing resistance and inductor. Thus by substituting the given values of effective resistance and inductive reactance, we could find the impedance of the given circuit. Now by using Ohm’s law, we could find the maximum current drawn from the circuit.
Formula used:
Expression for impedance,
$Z=\sqrt{{{R}^{2}}+{{X}_{L}}^{2}}$

Complete answer:
In the question, we are given an electric motor with an effective resistance of $30\Omega$ and an inductive reactance of $40\Omega$. Let the motor be powered by a source of maximum voltage $420V$, then, we are asked to find the maximum current in the circuit.
From the given value of effective resistance and inductive reactance we could find the effective impedance from the following equation,
$Z=\sqrt{{{R}^{2}}+{{X}_{L}}^{2}}$
Substituting the values we get,
$Z=\sqrt{{{30}^{2}}+{{40}^{2}}}$
$\Rightarrow Z=\sqrt{900+1600}$
$\therefore Z=50\Omega$
Now we could recall the ohm’s law which is given by,
$V=IR$
But here the R will be the effective impedance of the circuit and the voltage V will be the maximum voltage given in the question for $I$ to be the maximum current drawn from the circuit.
So,
${{I}_{\max }}=\dfrac{{{V}_{\max }}}{Z}$
Substituting the given values,
${{I}_{\max }}=\dfrac{420}{50}$
$\therefore {{I}_{\max }}=8.4A$
Therefore, we found the maximum current drawn from the circuit to be 8.4A.
Hence, option B is found to be the right answer.

Note:
Impedance just like resistance is the measure of the total opposition offered by the circuit to the current flow. The difference between impedance and resistance is that the impedance takes the effects of inductance as well as capacitance into account. The SI unit of impedance is also ohm. For an LCR circuit, it is given by,
$Z=\sqrt{{{R}^{2}}+{{\left( {{X}_{L}}-{{X}_{C}} \right)}^{2}}}$