Types of Ac Circuits > Circuit Containing Resistance Only

An alternating current (AC) circuit's behaviour — specifically the phase relationship between voltage and current — depends on whether the circuit contains a resistor, inductor, capacitor, or a combination of these elements. This module covers the simplest case: a circuit containing resistance only, which forms the foundation for understanding more complex RL, RC, and RLC circuits.

A purely resistive AC circuit consists of a non-inductive resistor R connected directly across an alternating voltage source, with no inductor or capacitor present in the circuit.

Step 1: Applied voltage: The alternating voltage applied across the resistor is given by

where V₀​ is the peak voltage, and ω is the angular frequency.

Step 2: Apply Ohm's Law: Since Ohm's law holds instantaneously for a pure resistor, V = IR.

Step 3: Solve for current:

• I = \[\frac {V_0}{R}\]sin ⁡(ωt) = I₀ sin ⁡(ωt)

where I₀ = \[\frac {V_0}{R}\]​​ is the peak (maximum) current.

Peak current depends only on resistance — not on frequency, unlike inductive or capacitive circuits.

• Current and voltage reach their maximum, minimum, and zero values at the same instant — i.e., they are in phase.
• Both quantities have the same frequency.
• Phase difference ϕ = 0.

Real-Life Analogy: Think of a simple incandescent bulb or an electric heater connected to a household AC supply — being purely resistive loads, the current drawn rises and falls exactly in step with the voltage, unlike a fan motor (inductive load) where current lags behind.