Concept explainers
In the circuit of Fig. 7.93,
- (a) Find R, L, and τ.
- (b) Calculate the energy dissipated in the resistance for 0 < t < 0.5 ms.
Figure 7.93
For Prob. 7.13.
(a)
Find the value of resistance R, inductance L and also find the time constant
Answer to Problem 13P
The value of resistance R in the circuit is
Explanation of Solution
Given data:
The voltage
The current
Formula used:
Write the general expression to find the voltage across the resistor using Ohms law.
Here,
Write the expression to find the time constant for RL circuit.
Here,
R is the resistance of the resistor, and
L is the inductance of the inductor.
Write the general expression to find the voltage response in the RL Circuit.
Here,
Calculation:
Substitute
Rearrange the above equation to find resistance R.
Compare the given voltage
Rearrange the equation (4) to find the time constant
Substitute
Rearrange the equation (5) to find the inductance L in Henry.
Conclusion:
Thus, the value of resistance R in the circuit is
(b)
Find the value of energy dissipated in the resistance for
Answer to Problem 13P
The value of energy dissipated in the resistance for
Explanation of Solution
Given data:
The energy dissipated in the resistance for the time limits
Formula used:
Write the expression to find the energy dissipated in the resistor.
Here,
Write the expression to find the power dissipated in the resistor.
Here,
Substitute equation (7) in equation (6) to find the energy dissipated in the resistor w.
Calculation:
Substitute
Rewrite the equation (9) as follows,
Reduce the equation (10) to find the energy dissipated in the resistor w in joules.
Converting the unit J to
Conclusion:
Thus, the value of energy dissipated in the resistance for
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Chapter 7 Solutions
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