Question

Calculate the inductance of a coil if a current that is changing at 10A/s induces an emf of thr 6,6V in the coil.

Answer 1

The inductance \( L \) of a coil can be calculated using Faraday's law of electromagnetic induction, which relates the induced electromotive force (emf) in a coil to the rate of change of current. The formula is given by:

\[
\text{emf} = -L \frac{di}{dt}
\]

where:
- \( \text{emf} \) is the induced electromotive force in volts (V),
- \( L \) is the inductance in henries (H),
- \( \frac{di}{dt} \) is the rate of change of current in amperes per second (A/s).

Rearranging this equation to solve for inductance \( L \), we have:

\[
L = -\frac{\text{emf}}{\frac{di}{dt}}
\]

In this case, the emf is given as 6.6 V and the rate of change of current \( \frac{di}{dt} \) is given as 10 A/s. Substituting these values into the equation:

\[
L = -\frac{6.6}{10}
\]

Calculating this gives:

\[
L = -0.66 \, \text{H}
\]

The negative sign indicates that the direction of the induced emf opposes the change in current (according to Lenz's law), but the magnitude of the inductance is typically reported as a positive value. Therefore, the inductance of the coil is:

\[
L = 0.66 \, \text{H}
\]