In the diagram is shown an RL circuit with a switch. ? = 105.0 V , R 1 = 60.0 ?
ID: 1374928 • Letter: I
Question
In the diagram is shown an RL circuit with a switch. ? = 105.0 V, R1 = 60.0 ?, R2 = 120.0 ? 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? 1.75A
What is i2 just after the switch is closed? 0.00A
What is the value of the current in the switch just after the switch is closed? 1.75A
What is the the potential difference across R2 just after the switch is closed? 0.00A
What is the the potential difference across L just after the switch is closed? 105V
PART 2: THIS IS WHAT NEEDS TO BE SOLVED
1. What is the rate of change of the current di2/dt in the time just after the closing of the switch?
2. What is i1 a long time after the switch is closed?
3. What is i2 a long time after the switch is closed?
4. What is the value of the current in the switch a long time after the switch is closed?
5. What is the the potential difference across R2 a long time after the switch is closed?
6. What is the the potential difference across L a long time after the switch is closed?
7. What is the rate of change of the current di2/dt a long time after the closing of the switch?
In the diagram is shown an RL circuit with a switch. ? = 105.0 V, R1 = 60.0 ?, R2 = 120.0 ? 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? 1.75A What is i2 just after the switch is closed? 0.00A What is the value of the current in the switch just after the switch is closed? 1.75A What is the the potential difference across R2 just after the switch is closed? 0.00A What is the the potential difference across L just after the switch is closed? 105V PART 2: THIS IS WHAT NEEDS TO BE SOLVED 1. What is the rate of change of the current di2/dt in the time just after the closing of the switch? 2. What is i1 a long time after the switch is closed? 3. What is i2 a long time after the switch is closed? 4. What is the value of the current in the switch a long time after the switch is closed? 5. What is the the potential difference across R2 a long time after the switch is closed? 6. What is the the potential difference across L a long time after the switch is closed? 7. What is the rate of change of the current di2/dt a long time after the closing of the switch?Explanation / Answer
1) i1 (the current in R1). This is calculated as V/R1 where V is the applied voltage of 105v i1 = 105/60 = 1.75A. This current does not change with time.
2) i2 (the common current in L and R2). At the moment that the switch is closed the current in L is assumed to be zero (see above). I2 = 0. When a voltage is applied to an inductor the rate of change of current is calculated as dI/dt = v/L. The current itself is not calculable. An initial current must either be known or assumed and I have assumed this to be zero. So the initial value of i2 is actually an assumption rather than a calculation. Since it is not specified in the question, you could, in principle, give any value to this current. This question is like asking 'what is the speed of a mass m at the moment that a force F is applied?'. We can say what the acceleration is, but we cannot say what the speed is - it might be anything.
3) the current through the switch. This is equal to i1:- 4A
4) the potential difference across R2. The initial current in this component is assumed to be zero, so this voltage is also 0
5) the pd across L at the moment the switch is closed is 105v. This is because at this time the current through L and therefore also through R2 is assumed to be zero. Therefore the pd across R2 is zero and the full supply voltage appears across L