Question

A series AC circuit has a resistance of 4Ω and a reactance of 3Ω. The impedance of the circuit is
A. 5Ω
B. 7Ω
C. $\frac{12}{7}$Ω
D. $\frac{7}{12}\Omega $

Answer 1

Hint: This is a direct question in which by knowing the relation between reactance, resistance and impedance we can easily solve it. The total resistance of an electric circuit to alternating current is called impedance. Here the values of resistance and reactance are given we only have to find the magnitude of impedance

Formula used:
Impedance,
$Z=\sqrt{{{R}^{2}}+{{X}^{2}}}$
Where, R is resistance and X is reactance.

Complete answer:
Resistance is defined as the measure of the opposition to current flowing in an electrical circuit. It is measured in ohms. Current and voltage is in phase in a pure resistance in ac circuit. Reactance has the same meaning of resistance. It is the measure of opposition to the flow of alternating current caused by the inductance and capacitance. Impedance is the effective measure of the opposition to the current flowing in a circuit. The sum of resistance and reactance is impedance. It is an AC characteristic of a circuit.

We have the equation of impedance as
Impedance, $Z=\sqrt{{{R}^{2}}+{{X}^{2}}}$
Where, R is resistance and X is reactance.
We have $Z=\sqrt{{{4}^{2}}+{{3}^{2}}}=5\Omega $

Therefore, the answer is (A)

Note: Note that resistance is real and reactance is imaginary. Therefore, impedance, which is the sum of resistance and reactance, is a complex number. But it has the same unit as resistance. That is ohm is the unit of impedance. It may vary with the operating frequency. The reactance offered by a capacitor of capacitance ‘C’ and inductor of inductance ‘L’ is different. It is commonly denoted as X. The reciprocal of impedance is admittance. The unit of admittance is siemens. It is also called mho.