Question

The plot of magnetic flux $\phi$ versus current I is shown for two inductors $L_{1}$ and $L_{2}$. The self inductance of}

• A. $L_{1}$ is equal to that of $L_{2}.$
• B. $L_{1}$ is less than that of $L_{2}$.
• C. $L_{1}$ is greater than that of $L_{2}$
• D. $L_{1}$ is half that of $L_{2}$.

Hint:

Steeper slope on a $\phi-I$ graph means higher self-inductance.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The graph shows magnetic flux (\( \phi \)) on the y-axis and current (\( I \)) on the x-axis for two different inductors.

Step 2: Key Formula or Approach:
The relationship between magnetic flux and current is given by:
\[ \phi = L I \] where \( L \) is the self-inductance.
From this linear relationship, the slope of the \( \phi \) vs \( I \) graph represents the self-inductance:
\[ \text{Slope} = \frac{\phi}{I} = L \]

Step 3: Detailed Explanation:
In the provided graph, the line for inductor \( L_1 \) makes a larger angle with the current axis (x-axis) than the line for inductor \( L_2 \).
\[ \theta_1 > \theta_2 \] Since the slope is equal to \( \tan \theta \):
\[ \tan \theta_1 > \tan \theta_2 \] Therefore, the self-inductance \( L_1 \) (slope of line 1) is greater than the self-inductance \( L_2 \) (slope of line 2).
\[ L_1 > L_2 \]

Step 4: Final Answer:
The self-inductance of \( L_1 \) is greater than that of \( L_2 \).