Physics · Alternating Current · NEET
No. Both an inductor and a resistor limit the current, but they do it differently. A resistor keeps current in phase with voltage and dissipates heat. A pure inductor makes the current lag the voltage by 90 degrees and dissipates NO average power. The opposition of an inductor is called inductive reactance XL = wL (unit: ohm), not resistance.
Start from Kirchhoff's loop rule: v = L (di/dt), so di/dt = (vm/L) sin(wt). Integrating gives i = -(vm/wL) cos(wt). Since -cos(wt) = sin(wt - pi/2), we get i = im sin(wt - pi/2). The '- pi/2' means the current reaches its peak a quarter cycle AFTER the voltage, so current lags voltage by 90 degrees.
Instantaneous power p = i*v = -(im*vm/2) sin(2wt). Over one full cycle the average of sin(2wt) is zero, so the average power is zero. Energy flows into the inductor's magnetic field for a quarter cycle and flows back out the next quarter cycle. This current that carries no net power is called the wattless current.
XL = wL = 2 pi f L. It is directly proportional to both the frequency f and the inductance L. So a higher frequency or a larger inductor gives more opposition. At f = 0 (pure DC steady state) XL = 0, so a pure inductor lets DC pass freely once current is steady.
It has the same unit (ohm) and limits current the same way (im = vm/XL), but it is NOT resistance. Resistance is fixed and dissipates energy; reactance XL changes with frequency and dissipates no average power. That is why we call XL reactance, not resistance.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
The current lags the voltage by 90 degrees (pi/2 radians), i.e. by one quarter of a cycle. Voltage peaks first, current peaks a quarter cycle later.
XL = wL = 2 pi f L, measured in ohms. It increases with both frequency and inductance.
im = vm / XL = vm / (wL). In rms terms, Irms = Vrms / XL.
Because current lags voltage by exactly 90 degrees, so cos(phi) = cos(90) = 0. Energy is stored in the magnetic field and returned each cycle, giving zero net average power (wattless current).
For steady DC, f = 0 so XL = wL = 0. The inductor offers no opposition and behaves like a plain wire once the current becomes steady.
