How many degrees are the current and voltage out of phase with each other in a pure resistive circuit?
The correct answer and explanation is :
In a pure resistive circuit, the current and voltage are 0 degrees out of phase with each other.
Explanation (Approx. 300 words):
In electrical circuits, phase difference refers to the angular displacement between the voltage waveform and the current waveform. This displacement is measured in degrees (°). A phase difference of 0° means both waveforms reach their peaks, zero crossings, and troughs at the same time.
In a purely resistive circuit, the circuit contains only resistance (such as a resistor) and no reactive components like inductors or capacitors. According to Ohm’s Law, which states that $V = IR$, the voltage across a resistor is directly proportional to the current flowing through it. This linear relationship means that both the voltage and the current waveforms will rise and fall together.
In an AC (alternating current) resistive circuit, both voltage and current waveforms are sinusoidal. Because there’s no energy storage (as there would be with capacitors or inductors), there is no phase shift introduced between the current and voltage. They are said to be “in phase”, meaning the current and voltage reach their maximum, minimum, and zero values at the same time.
Mathematically:
- Voltage: $V(t) = V_m \sin(\omega t)$
- Current: $I(t) = I_m \sin(\omega t)$
Here, both functions are sine waves with the same phase angle, so the phase difference is 0°.
This in-phase behavior has important implications in power calculations. For a purely resistive circuit, the power factor (which is the cosine of the phase angle) is:
$$
\text{Power Factor} = \cos(0^\circ) = 1
$$
A power factor of 1 means that all the power supplied by the source is used by the load as real power, with no reactive (wasted) power.
In contrast, inductive or capacitive circuits do show phase shifts due to energy being temporarily stored and released by the field components.
Answer: 0 degrees — in a pure resistive circuit, voltage and current are in phase.