Concept explainers
(a)
The current in the windings.
(a)
Answer to Problem 53P
The current in the windings is
Explanation of Solution
Given that the voltage offered by the power supply is
The equilibrium current in the circuit is equal to the maximum current flowing through the winding.
Write the expression for the maximum current through the winding.
Here,
Conclusion:
Substitute
Therefore, the current in the windings is
(b)
The need of the shunt resistor in the
(b)
Answer to Problem 53P
The shunt resistor reduces the rate of change of current in the winding of the electromagnet, and hence allowing the electromagnet to shut off safely. The shunting action is possible only if the shunt resistor is connected in the circuit before disconnecting the power supply.
Explanation of Solution
If the power supply to the electromagnet is stopped suddenly, then the induced emf in the windings will be very large so that there is a possibility of damaging of the winding itself. Moreover, it is likely that sparks would complete the circuit across the open switch.
The presence of a shunt resistor reduces the rate of change of current in the winding of the electromagnet, and hence allowing the electromagnet to shut off safely. In order to have the effect of the shunt resistor in the process, it must be present in the circuit before switching off the power supply. Simply, the shunt resistor must be connected before disconnecting the power supply.
Conclusion:
Therefore, the shunt resistor reduces the rate of change of current in the winding of the electromagnet, and hence allowing the electromagnet to shut off safely. The shunting action is possible only if the shunt resistor is connected in the circuit before disconnecting the power supply.
(c)
The maximum power dissipated in the shunt resistor.
(c)
Answer to Problem 53P
The maximum power dissipated in the shunt resistor is
Explanation of Solution
Given that the resistance of the shunt resistor is
Write the expression for the maximum power dissipated in a resistor.
Here,
Conclusion:
Substitute
Therefore, the maximum power dissipated in the shunt resistor is
(d)
The time taken for the current in the windings to drop to
(d)
Answer to Problem 53P
The time taken for the current in the windings to drop to
Explanation of Solution
Given that the resistance of the shunt resistor is
When the switch
Write the expression for the current in an
Here,
Solve equation (III) for
Write the expression for the time constant of the
Here,
Write the expression for the equivalent resistance in the given circuit.
Use equation (VI) in (V).
Use equation (VII) in (IV).
Conclusion:
Substitute
Therefore, the time taken for the current in the windings to drop to
(e)
Whether a large shunt resistor would dissipate the energy stored in the electromagnet faster or not.
(e)
Answer to Problem 53P
A large shunt resistor would dissipate the energy stored in the electromagnet faster.
Explanation of Solution
According to equation (VIII), the time taken for the dissipation of current in the winding is inversely proportional to the equivalent resistance of the circuit.
If the shunt resistance value is increased, then the equivalent resistance of the circuit increases. This results the time taken for the current dissipation in the winding or the electromagnet decrease. That is, a large shunt resistor would dissipate the energy stored in the electromagnet faster
Conclusion:
Therefore, a large shunt resistor would dissipate the energy stored in the electromagnet faster.
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Chapter 20 Solutions
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