Question:
If a solenoid has \(500\) turns, length \(0.5\,\text{m}\) and cross-sectional area \(4\times10^{-4}\,\text{m}^2\), then its self-inductance is
If a solenoid has \(500\) turns, length \(0.5\,\text{m}\) and cross-sectional area \(4\times10^{-4}\,\text{m}^2\), then its self-inductance is
Show Hint
For a long solenoid,
\[
\boxed{
L=\frac{\mu_0N^2A}{l}
}
\]
where \(N\) is the number of turns, \(A\) is the cross-sectional area and \(l\) is the length.
Updated On: Jul 14, 2026
- \(0.25\,\text{mH}\)
- \(0.63\,\text{mH}\)
- \(1.26\,\text{mH}\)
- \(2.5\,\text{mH}\)
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Use the formula for self-inductance of a solenoid.
\[
L=\frac{\mu_0N^2A}{l},
\]
where
\[
\mu_0=4\pi\times10^{-7}\,\text{H/m},
\]
\[
N=500,\qquad
A=4\times10^{-4}\,\text{m}^2,\qquad
l=0.5\,\text{m}.
\]
Step 2: Substitute the values. \[ L= \frac{4\pi\times10^{-7}\times(500)^2\times4\times10^{-4}}{0.5} \] \[ =1.26\times10^{-3}\,\text{H} =1.26\,\text{mH}. \] Hence, \[ \boxed{1.26\,\text{mH}} \] Therefore, \[ \boxed{(C)} \] is the correct answer.
Step 2: Substitute the values. \[ L= \frac{4\pi\times10^{-7}\times(500)^2\times4\times10^{-4}}{0.5} \] \[ =1.26\times10^{-3}\,\text{H} =1.26\,\text{mH}. \] Hence, \[ \boxed{1.26\,\text{mH}} \] Therefore, \[ \boxed{(C)} \] is the correct answer.
Was this answer helpful?
0
0
Top TS PGECET Instrumentation Engineering Questions
- The energy stored in a capacitor \( C \) when a voltage \( V \) exists across it is:
- The mechanical force per unit charge at a given point is called:
- Force on a current-carrying conductor placed in a magnetic field is given by:
- "Whenever magnetic flux linked with a closed coil changes, an induced emf is setup in the coil and lasts as long as the change in magnetic flux continues." This is:
- Internal resistance of an ideal voltage source is:
View More Questions
Top TS PGECET Basics of Circuits Questions
- The energy stored in a capacitor \( C \) when a voltage \( V \) exists across it is:
- The mechanical force per unit charge at a given point is called:
- Force on a current-carrying conductor placed in a magnetic field is given by:
- "Whenever magnetic flux linked with a closed coil changes, an induced emf is setup in the coil and lasts as long as the change in magnetic flux continues." This is:
- Internal resistance of an ideal voltage source is:
View More Questions
Top TS PGECET Questions
- If \( P = \begin{pmatrix} 1 & 1 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 1 \end{pmatrix} \) is the modal matrix of \( A = \begin{pmatrix} 1 & 1 & 0 \\ 0 & 2 & 2 \\ 0 & 0 & 3 \end{pmatrix} \) then the sum of all the elements of \( P^{-1}AP \) is
- If the system of equations \( kx + y + z = k - 1 \), \( x + ky + z = k - 1 \), and \( x + y + kz = k - 1 \) has infinite solutions, then \( k \) is
- The value of the integral \( \int_C (2xy - x^2) \, dx + (x^2 + y^2) \, dy \) where \( C \) is the boundary of the region enclosed by \( y = x^2 \) and \( y^2 = x \), described in the positive sense, is
- Let \( f(x) = \log x \). The number \( C \) strictly between \( e^2 \) and \( e^3 \) such that its reciprocal is equal to \( \frac{f(e^3) - f(e^2)}{e^3 - e^2} \) is
- The solution of the differential equation \( (D^2 + 2)y = x^2 \) is
View More Questions