Question

In a circuit containing a pure resistor connected to an AC source,

• A. Voltage leads the current by 90\(^{\circ}\)
• B. Current leads the voltage by 90\(^{\circ}\)
• C. Voltage and current are in same phase with each other
• D. Current leads the voltage by 180\(^{\circ}\)

Hint:

Use the mnemonic \textbf{CIVIL}:
- In a \textbf{C}apacitor, \textbf{I} (current) leads \textbf{V} (voltage).
- In an \textbf{I}nductor (\textbf{L}), \textbf{V} (voltage) leads \textbf{I} (current).
- For a Resistor, they are "together" (in phase).

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks about the phase relationship between the instantaneous voltage and the instantaneous current in a purely resistive AC circuit.
Step 3: Detailed Explanation:
Let the alternating voltage from the source be represented as:
\[ v = V_m \sin(\omega t) \]
According to Ohm's Law, the instantaneous current \( i \) through a resistor with resistance \( R \) is:
\[ i = \frac{v}{R} = \frac{V_m}{R} \sin(\omega t) \]
We can write this as \( i = I_m \sin(\omega t) \), where \( I_m = \frac{V_m}{R} \).
Comparing the expressions for \( v \) and \( i \), we see that both have the same phase angle (\( \omega t \)). This means that they reach their maximum, minimum, and zero values at the same time. Therefore, the voltage and current are in phase.
Step 4: Final Answer:
In a pure resistor, voltage and current are in the same phase with each other, which corresponds to option (3).