A 10 Henry inductor carries a Steady Current of 2 ampere. How can a 10...
Induced emf in inductor is given by
e = -LdI/dt
L = 10 H, e = 100 V,
we can calculate the rate of change of current (dI/dt)
100 = -10 x dI/dt
dI/dt = - 10
(0 - 2)/dt = - 10
dt = 2/10 = 0.2 second.
Thus if we change the current to zero in 0.2 s, we can induce 100 V emf across the inductor.
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A 10 Henry inductor carries a Steady Current of 2 ampere. How can a 10...
Introduction:
To generate a self-induced electromotive force (EMF) of 100 volts in a 10 Henry inductor carrying a steady current of 2 amperes, we can make use of Faraday's law of electromagnetic induction. According to this law, a change in the magnetic field through a circuit induces an EMF in the circuit.
Steps to create a 100 volt self-induced EMF:
1. Change in Current:
- The self-induced EMF can be generated by changing the current flowing through the inductor.
- To achieve this, we can connect a switch in series with the inductor.
- Initially, the switch is open, and the inductor carries a steady current of 2 amperes.
2. Closing the Switch:
- When the switch is closed, the circuit is completed, allowing the current to flow through the inductor.
- As the current starts to flow, the magnetic field around the inductor begins to change.
3. Change in Magnetic Field:
- As the current changes, the magnetic field through the inductor also changes.
- This change in magnetic field induces an electromotive force (EMF) in the inductor according to Faraday's law.
4. Calculation of Self-Induced EMF:
- The self-induced EMF can be calculated using the formula: EMF = -L * (di/dt), where L is the inductance and (di/dt) is the rate of change of current.
- Given that the inductance is 10 Henry and the initial current is 2 amperes, we need to calculate the rate of change of current.
5. Rate of Change of Current:
- Let's assume that the current changes linearly with time.
- If the current changes from 2 amperes to 0 amperes in t seconds, then the rate of change of current is (0 - 2)/t = -2/t amperes per second.
6. Substituting values:
- Substituting the values into the formula, we get: EMF = -10 * (-2/t).
- Simplifying further, EMF = 20/t volts.
7. Choosing the Time Interval:
- To generate a self-induced EMF of 100 volts, we need to choose an appropriate time interval.
- Let's assume we want the self-induced EMF to reach 100 volts within 5 seconds.
8. Final Calculation:
- Substituting the chosen time interval into the formula, we get: EMF = 20/5 = 4 volts per second.
- Therefore, to generate a 100 volt self-induced EMF, the current should decrease at a rate of 4 amperes per second.
Conclusion:
By closing the switch and allowing the current to decrease at a rate of 4 amperes per second, a self-induced EMF of 100 volts can be generated in the 10 Henry inductor, as per Faraday's law of electromagnetic induction.