A graph of magnetic flux (\( \phi \)) versus current (\( I \)) is shown for four inductors P, Q, R, S. The largest value of self-inductance is for inductor}
Step 1: Understanding the Concept:
Self-inductance \( L \) is a property of an inductor that describes its ability to oppose changes in current.
It is defined as the ratio of magnetic flux linkage \( \phi \) to the current \( I \) flowing through the coil. Step 2: Key Formula or Approach:
The defining equation for self-inductance is:
\[ \phi = L \cdot I \]
where \( \phi \) is the magnetic flux, \( L \) is the self-inductance, and \( I \) is the current.
Rearranging this equation, we get:
\[ L = \frac{\phi}{I} \]
Step 3: Detailed Explanation:
The given graph plots magnetic flux \( \phi \) on the y-axis and current \( I \) on the x-axis.
Comparing the relation \( \phi = L \cdot I \) with the equation of a straight line passing through the origin, \( y = mx \), we can identify that the slope \( m \) of the graph corresponds to the self-inductance \( L \).
Slope \( = \frac{\Delta y}{\Delta x} = \frac{\Delta \phi}{\Delta I} = L \).
Therefore, the inductor with the steepest slope (largest angle with the x-axis) will have the largest value of self-inductance.
Observing the given lines P, Q, R, and S from the origin:
Line P has the maximum inclination or steepest slope.
Line S has the minimum inclination or least slope.
Since line P has the maximum slope, it represents the inductor with the largest self-inductance. Step 4: Final Answer:
The largest value of self-inductance is for inductor P.
