In the diagram is shown an RL circuit with a switch. ? = 95.0 V , R 1 = 40.0 ? ,
ID: 1453759 • Letter: I
Question
In the diagram is shown an RL circuit with a switch. ? = 95.0 V, R1 = 40.0 ?, R2 = 80.0 ? and L = 60.0 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 i2 just after the switch is closed?
What is the value of the current in the switch 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?
Explanation / Answer
When we close the switch just after that the current in inductor won't change and it will be zero as earlier it was.
Hence i2 = 0.
The circuit including inductor will work as a open circuit, hence the current i1 will be i1 = E/R1 = 95/40 = 2.375 A
So current in switch will be equal to i1+i2 = 2.375 A
The current in R2 is zero hence the potential difference will be zero across R2. and so the potential difference across L will equal to E which is 95 V.
So L di_2/dt = 95
so di_2/dt = 95/60 = 1.58 A/s
After a long time the inductor will work as a short circuit,
So, i1 will remain same which is 2.375 A
i2 will be 95/80 = 1.19 A
Current in the switch will be 3.565 A
Potential difference across R2 will be 95 V
potential difference across L will be 0
Hence the rate of change of current di_2/dt will be zero.