Two coils have a mutual inductance of 0.2H. If the current in one coil is changed from 10A to 4A in 10ms, calculate (a) the induced emf in the second coil (b) the change of flux li... Two coils have a mutual inductance of 0.2H. If the current in one coil is changed from 10A to 4A in 10ms, calculate (a) the induced emf in the second coil (b) the change of flux linked with the second coil if it is wound with 500 turns.
Understand the Problem
The question is asking to calculate the induced electromotive force (emf) in a second coil and the change of flux linked with that coil, given specific parameters about the mutual inductance, the change in current of one coil, and the number of turns in the second coil. We will apply the formulas for mutual inductance and induced emf to solve for the required values.
Answer
- Change in Magnetic Flux: $ \Delta \Phi = M \cdot \Delta I $ - Induced emf: $ \text{emf} = -N_2 \cdot \frac{M \cdot \Delta I}{\Delta t} $
Answer for screen readers
The final answer will depend on the specific values provided earlier in the question.
To express it in formula format:
-
Change in Magnetic Flux: $$ \Delta \Phi = M \cdot \Delta I $$
-
Induced emf: $$ \text{emf} = -N_2 \cdot \frac{M \cdot \Delta I}{\Delta t} $$
Steps to Solve
- Identify the Given Data
We know the following parameters:
- Mutual inductance, $M$ (in henries)
- Change in current, $\Delta I$ (in amperes)
- Number of turns in the second coil, $N_2$
- Calculate the Change in Magnetic Flux
The change in magnetic flux, $\Delta \Phi$, linked with the second coil can be calculated using the formula: $$ \Delta \Phi = M \cdot \Delta I $$
- Calculate the Induced Electromotive Force (emf)
The induced emf in the second coil can be found using the formula: $$ \text{emf} = -N_2 \cdot \frac{\Delta \Phi}{\Delta t} $$ where $\Delta t$ is the time over which the change occurs.
- Substitute and Solve
Finally, plug in the values for $M$, $\Delta I$, $N_2$, and $\Delta t$ into the above formula for induced emf to get the final answer.
The final answer will depend on the specific values provided earlier in the question.
To express it in formula format:
-
Change in Magnetic Flux: $$ \Delta \Phi = M \cdot \Delta I $$
-
Induced emf: $$ \text{emf} = -N_2 \cdot \frac{M \cdot \Delta I}{\Delta t} $$
More Information
This calculation uses the principles of mutual inductance, which describes how a change in current in one coil can induce electromotive force in another coil nearby. The negative sign in the induced emf equation follows Lenz's Law, indicating the direction of induced current will oppose the change causing it.
Tips
- Forgetting to include the negative sign in the emf formula related to Lenz's Law.
- Not using the correct units for each variable, which can lead to calculation errors.
- Failing to carefully convert values when needed (e.g., converting milliseconds to seconds).
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