Question:
The ratio of the turns per unit length in two inductors is
\[
2:1.
\]
Then the ratio of the impedances produced by the inductors is
The ratio of the turns per unit length in two inductors is
\[
2:1.
\]
Then the ratio of the impedances produced by the inductors is
Show Hint
For a solenoid,
\[
L=\mu_0 n^2Al.
\]
Therefore,
\[
L\propto n^2
\]
and at a fixed frequency,
\[
X_L=\omega L\propto n^2.
\]
If turns per unit length double, inductive reactance becomes four times.
Updated On: Jul 29, 2026
- \(2\)
- \(4\)
- \[ \frac{1}{2} \]
- \[ \frac{1}{4} \]
Show Solution
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The Correct Option is B
Solution and Explanation
Concept:
The inductive reactance (impedance due to an inductor) is
\[
X_L=\omega L.
\]
For a long solenoid,
\[
L=\mu_0 n^2Al,
\]
where
\[
n=\text{number of turns per unit length}.
\]
Hence,
\[
L\propto n^2.
\]
Since
\[
X_L=\omega L,
\]
for the same frequency,
\[
X_L\propto n^2.
\]
Step 1: Write the given ratio. \[ n_1:n_2=2:1. \]
Step 2: Find the ratio of inductances. \[ L_1:L_2 = n_1^2:n_2^2. \] \[ = 2^2:1^2. \] \[ = 4:1. \]
Step 3: Find the ratio of impedances. Since \[ X_L\propto L, \] \[ X_{L1}:X_{L2} = 4:1. \] Therefore, \[ \boxed{\frac{X_{L1}}{X_{L2}}=4} \] \[ \boxed{\text{Answer = (B)}} \]
Step 1: Write the given ratio. \[ n_1:n_2=2:1. \]
Step 2: Find the ratio of inductances. \[ L_1:L_2 = n_1^2:n_2^2. \] \[ = 2^2:1^2. \] \[ = 4:1. \]
Step 3: Find the ratio of impedances. Since \[ X_L\propto L, \] \[ X_{L1}:X_{L2} = 4:1. \] Therefore, \[ \boxed{\frac{X_{L1}}{X_{L2}}=4} \] \[ \boxed{\text{Answer = (B)}} \]
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