Physics · Alternating Current · NEET
Power factor is the number cos φ. In an AC circuit the voltage and current are usually out of step by an angle φ. Real power used is P = V I cos φ, where V and I are rms values. So power factor is the 'fraction' of V x I that becomes real work or heat. If cos φ = 1, all of V x I is used. If cos φ = 0, none of it is used (no power lost), even though current still flows. That is why it matters for NEET: it decides how much power a circuit actually consumes.
Average power over one cycle works out to P = V I cos φ, so cos φ is the factor sitting in front. In a series LCR circuit, draw the impedance triangle: R is the base, net reactance (X_L - X_C) is the height, and impedance Z is the hypotenuse. The angle between R and Z is the same phase angle φ. So cos φ = adjacent/hypotenuse = R/Z. Both forms are the same quantity. Use cos φ = R/Z when you know R and Z, and use cos φ = V_R/V when you know voltages.
No. Phase angle φ is the angle (in degrees or radians) between voltage and current. Power factor is cos φ, a pure number with no unit, always between 0 and 1 in magnitude. Example: if φ = 60 degrees, power factor = cos 60 = 0.5. NEET questions often give you φ and expect cos φ, or give you cos φ and expect φ. Do not confuse the angle with its cosine.
In a pure inductor current lags voltage by 90 degrees; in a pure capacitor current leads voltage by 90 degrees. Either way φ = 90 degrees, so cos φ = cos 90 = 0. Then P = V I cos φ = 0. No average power is dissipated even though current flows. This current is called wattless current. Real components have some resistance, so real coils do lose a little power, but the ideal L or C loses none.
At resonance X_L = X_C, so the net reactance is zero. Then Z = R, and cos φ = R/Z = R/R = 1. The circuit behaves purely resistive, φ = 0, and maximum power is dissipated. Any NEET question that says 'X_L = X_C' or 'at resonance' is telling you power factor = 1 directly.
The potential differences across the resistance, capacitance and inductance are 80 V, 40 V and 100 V respectively in an L-C-R circuit. The power factor of this circuit is
A series LCR circuit is connected to an ac voltage source. When L is removed from the circuit, the phase difference between current and voltage is π/3. If instead C is removed, the phase difference is again π/3. The power factor of the circuit is
To an ac power supply of 220 V at 50 Hz, a resistor of 20 Ω, a capacitor of reactance 25 Ω and an inductor of reactance 45 Ω are connected in series. The current in the circuit 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.
Power factor = cos φ = R/Z, where R is resistance and Z is impedance. Equivalent forms are cos φ = V_R/V (resistor voltage over source voltage) and P = V I cos φ, so cos φ = real power / (V x I).
No. Power factor is cos φ, and the cosine of any angle lies between −1 and 1. Its magnitude is always 0 to 1. A value of exactly 1 means a purely resistive circuit.
It is 1. In a pure resistor voltage and current are in phase, so φ = 0 and cos φ = 1. Maximum power is dissipated, which is why resistive circuits are the answer to 'where is maximum power dissipated in AC'.
Wattless current is the component of current that is 90 degrees out of phase with the voltage. It carries no average power because for it cos φ = 0. A pure inductor or pure capacitor carries wattless current.
To deliver a fixed power P at fixed voltage V, current I = P/(V cos φ). A small cos φ forces a large current, and line heating loss is I²R, so the loss grows. That is why power companies add capacitors to push power factor near 1.
