Question

L, C and R are connected in series to an a.c. source. Which one of the following is true? Phase relation between current and voltage is such that ______.

• A. both are out of phase with each other in 'R'.
• B. both are in phase in 'L' and out of phase in 'C'.
• C. both are out of phase in 'L' and in phase in 'C'.
• D. both are out of phase in both 'C' and 'L'.

Hint:

Memorize the acronym ELI the ICE man:
E L I: In an Inductor (L), voltage (EMF) leads current (I).
I C E: In a Capacitor (C), current (I) leads voltage (EMF).

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The question asks us to identify the correct phase relationships between Alternating Current (AC) and Voltage specifically across the individual passive components (Resistor, Inductor, and Capacitor).

Step 2: Detailed Explanation:
Let's review the fundamental AC phase rules for each ideal component:
1. Resistor ('R'):
According to Ohm's law ($V = IR$), the voltage across a resistor is directly proportional to the current at every instant. They rise and fall together.
Therefore, voltage and current are exactly IN PHASE in 'R' ($\Delta\phi = 0^\circ$).
- This makes option (a) FALSE.
2. Inductor ('L'):
An inductor opposes changes in current ($V = L \frac{di}{dt}$). This creates a delay. The voltage reaches its maximum before the current does.
Voltage LEADS current by exactly $90^\circ$ ($\pi/2$ rad).
Therefore, voltage and current are OUT OF PHASE in 'L'.
3. Capacitor ('C'):
A capacitor must draw current first in order to build up voltage across its plates ($V = \frac{1}{C} \int i \, dt$).
Voltage LAGS current by exactly $90^\circ$ ($\pi/2$ rad).
Therefore, voltage and current are OUT OF PHASE in 'C'.
Combining these facts: Voltage and current are strictly out of phase in both 'C' and 'L'.

Step 3: Final Answer:
Both are out of phase in both 'C' and 'L', matching option (d).