Physics · Alternating Current · NEET
Because R, X_L and X_C are not in phase, so you cannot add them like ordinary numbers. The voltage across R is in phase with current, the voltage across L leads current by 90 degrees, and the voltage across C lags by 90 degrees. Adding them needs vector (phasor) addition, which gives Z = sqrt(R^2 + (X_L - X_C)^2), not a plain sum.
The inductor and capacitor act in opposite directions. Inductor voltage points up (+90 degrees) and capacitor voltage points down (-90 degrees) in the phasor diagram. They are along the same line but opposite, so the net reactance is their difference X_L - X_C. In the formula it is squared, so it does not matter which is bigger; sqrt((X_L - X_C)^2) is the same as sqrt((X_C - X_L)^2).
The unit of impedance is the ohm (same as resistance), because impedance is voltage divided by current: Z = V_rms / I_rms. A larger Z means the circuit lets less current flow for the same voltage.
At resonance X_L = X_C, so X_L - X_C = 0. The formula reduces to Z = sqrt(R^2 + 0) = R. Impedance becomes minimum and equals just the resistance, so the current is maximum. This is why resonance questions are so common in NEET.
Resistance R opposes current and dissipates energy as heat. Reactance (X_L or X_C) opposes current but stores and returns energy, no heat. Impedance Z is the combined opposition of both together. R and reactance are the sides; Z is the resultant.
An inductor L, capacitor C and resistor R are connected in series to an ac source. The potential differences across L, C and R are 40 V, 10 V and 40 V respectively. The current amplitude is 10*sqrt(2) A. The impedance of the circuit is:
A series circuit has R = 10 ohm, an inductor and a capacitor with X_L = 5 ohm and X_C = 10 ohm driven by an AC source. The net impedance of the circuit is:
To an ac supply of 220 V at 50 Hz, a resistor of 20 ohm, a capacitor of reactance 25 ohm and an inductor of reactance 45 ohm are connected in series. The current and the phase angle between current and voltage are respectively:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Z = sqrt(R^2 + (X_L - X_C)^2), where X_L = omega*L (inductive reactance) and X_C = 1/(omega*C) (capacitive reactance). The unit is the ohm.
The ohm, the same as resistance, because impedance is defined as Z = V_rms / I_rms (voltage divided by current).
Impedance is minimum at resonance, when X_L = X_C. Then Z = R, its smallest value, so the current is maximum.
No. Since Z = sqrt(R^2 + (X_L - X_C)^2), the term under the root is always at least R^2, so Z is always greater than or equal to R. The smallest possible value of Z is R, reached only at resonance.
Because R is drawn along the current direction and net reactance (X_L - X_C) is drawn at 90 degrees to it. The resultant of two perpendicular sides is the hypotenuse, so Z = sqrt(R^2 + (X_L - X_C)^2).
