http://imgur.com/SYTFgpK In the diagram is shown an RL circuit with a switch. =
ID: 1454926 • Letter: H
Question
http://imgur.com/SYTFgpK
In the diagram is shown an RL circuit with a switch. = 110.0 V, R1 = 75.0 , R2 = 150.0 and L = 45.0 H. Find the values of i1, the current through resistor R1 and i2, the current through resistor R2, the current through the switch, the potential difference across R2, the potential difference across L and the rate of change of the current di2/dt in the time just after the closing of the switch.
What is i1 just after the switch is closed?
What is the value of the current in the switch just after the switch is closed? What is i2 just after the switch is closed?
What is the the potential difference across R2 just after the switch is closed?
What is the the potential difference across L just after the switch is closed?
What is the rate of change of the current di2/dt in the time just after the closing of the switch?
What is i1 a long time after the switch is closed?
What is i2 a long time after the switch is closed?
What is the value of the current in the switch a long time after the switch is closed?
What is the the potential difference across R2 a long time after the switch is closed?
What is the the potential difference across L a long time after the switch is closed?
What is the rate of change of the current di2/dt a long time after the closing of the switch?
Explanation / Answer
1)
Just after the switch is closed the inductor acts like an open circuit
So
i2 = 0 i1 = E/R1 = 110/75 = 1.46666666 A
The current through the switch is i1 = 1.46666666 A
Since i2 = 0 V(R2) = 0V
V(L) = E = 110.0V
Using V(L) = L*di/dt we get di/dt = V(L)/L = 110.0V/45 = 2.4444A/s
2)
Just after the switch is closed the inductor acts like an open circuit
So
i2 = 0 i1 = E/R1 = 110/75 = 1.4666666 A
The current through the switch is i1 = 1.46666666 A
Since i2 = 0 V(R2) = 0V
V(L) = E = 110.0V
Using V(L) = L*di/dt we get di/dt = V(L)/L = 110.0V/45 = 2.444444A/s
The current through the switch is i1 = 1.4666666 A
3)
Just after the switch is closed the inductor acts like an open circuit
So
i2 = 0 i1 = E/R1 = 110/75 = 1.466666 A
The current through the switch is i1 = 1.4666666 A
Since i2 = 0 V(R2) = 0V
V(L) = E = 110.0V
Using V(L) = L*di/dt we get di/dt = V(L)/L = 110.0V/45 = 2.444444A/s
Since i2 = 0 V(R2) = 0V
4)
Just after the switch is closed the inductor acts like an open circuit
So
i2 = 0 i1 = E/R1 = 110/75 = 1.466666 A
The current through the switch is i1 = 1.4666666 A
Since i2 = 0 V(R2) = 0V
V(L) = E = 110.0V <<<<<<<+++++++++
Using V(L) = L*di/dt we get di/dt = V(L)/L = 110.0V/45 = 2.444444A/s
5)
Just after the switch is closed the inductor acts like an open circuit
So
i2 = 0 i1 = E/R1 = 110/75 = 1.466666 A
The current through the switch is i1 = 1.4666666 A
Since i2 = 0 V(R2) = 0V
V(L) = E = 110.0V
Using V(L) = L*di/dt we get di/dt = V(L)/L = 110.0V/45 = 2.44444A/s
6)
Just after the switch is closed the inductor acts like an open circuit
So
i2 = 0 i1 = E/R1 = 110/75 = 1.4666666 A
The current through the switch is i1 = 1.4666666 A
Since i2 = 0 V(R2) = 0V
V(L) = E = 110.0V
Using V(L) = L*di/dt we get di/dt = V(L)/L = 110.0V/45 = 2.44444A/s
The current through the switch is i1 = 1.4666666 A
A long time after the switch is closed the inductors acts like a short circuit:
So since the resistors are in parallel the voltage over each one is 110.0V
So i1 = V/R1 = 110.0/75 = 1.466666 A
7)
Just after the switch is closed the inductor acts like an open circuit
So
i2 = 0 i1 = E/R1 = 110/75 = 1.466666666 A
The current through the switch is i1 = 1.4666666 A
Since i2 = 0 V(R2) = 0V
V(L) = E = 110.0V
Using V(L) = L*di/dt we get di/dt = V(L)/L = 110.0V/45 = 2.4444444A/s
The current through the switch is i1 = 1.466666 A
A long time after the switch is closed the inductors acts like a short circuit:
So since the resistors are in parallel, the voltage over each one is the emf
so V(R2) = 110.0V
Therefore i2 = V(R2)/R2 = 110/150 = 0.7333333 A
8)
Just after the switch is closed the inductor acts like an open circuit
So
i2 = 0 i1 = E/R1 = 110/75 = 1.4666666 A
The current through the switch is i1 = 1.4666666 A
Since i2 = 0 V(R2) = 0V
V(L) = E = 110.0V
Using V(L) = L*di/dt we get di/dt = V(L)/L = 110.0V/45 = 2.4444444444A/s
The current through the switch is i1 = 1.46666666 A
A long time after the switch is closed the inductors acts like a short circuit:
So since the resistors are in parallel,
the equivalent resistance is R1*R2/(R1 + R2) = 75*150/(75+150) = 50
So i = V/R = 110/50 = 2.2 A
9)
Just after the switch is closed the inductor acts like an open circuit
So
i2 = 0 i1 = E/R1 = 110/75 = 1.466666 A
The current through the switch is i1 = 1.466666666 A
Since i2 = 0 V(R2) = 0V
V(L) = E = 110.0V
Using V(L) = L*di/dt we get di/dt = V(L)/L = 110.0V/45 = 2.44444444A/s
The current through the switch is i1 = 1.4666666666 A
A long time after the switch is closed the inductors acts like a short circuit:
So since the resistors are in parallel, the voltage over each one is the emf
so V(R2) = 110.0V
10)
Just after the switch is closed the inductor acts like an open circuit
So
i2 = 0 i1 = E/R1 = 110/75 = 1.4666666666 A
The current through the switch is i1 = 1.4666666666 A
Since i2 = 0 V(R2) = 0V
V(L) = E = 110.0V
Using V(L) = L*di/dt we get di/dt = V(L)/L = 110.0V/45 = 2.44444A/s
The current through the switch is i1 = 1.466666666 A
A long time after the switch is closed the inductors acts like a short circuit:
So since V = I*R and R = 0 then
V = 0
11)
Since the inductor acts like a short circuit a long time after the switch closes, the voltage over the inductor is 0
and since V = L*di2/dt then di2/dt = 0
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