In the diagram is shown an RL circuit with a switch. ? = 85.0 V , R 1 = 35.0 ? ,
ID: 1451645 • Letter: I
Question
In the diagram is shown an RL circuit with a switch. ? = 85.0 V, R1 = 35.0 ?, R2 = 70.0 ? and L = 50.0 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 rate of change of the current di2/dt in the time just after the closing of the switch? What is the the potential difference across L just after the switch is closed?
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 rate of change of the current di2/dt a long time after the closing of the switch?What is the the potential difference across R2 a long time after the switch is closed?
Explanation / Answer
I have copied part of your question in order to make it easier for me to understand it -
Find the values of the following at the moment the switch is closed:-
1) i1, the current through resistor R1 and
2) i2, the current through resistor R2,
3) the current through the switch,
4) the potential difference across R2,
5) the potential difference across L
6) the rate of change of the current di2/dt in the time just after the closing of the switch.
7) What is the the potential difference across L a long time after the switch is closed?
In answering this question I shall assume that L is an ideal inductor having no resistance, and that at the moment immediately before the switch is closed, the current in the loop consisting of R1, R2 and L is zero. The latter condition is not stated in the question, and is not necessarily true, since L can act as a source of emf which would drive a current around this loop even in the absence of the 85 V supply. This is an assumed initial condition and my results depend on it.
1) i1 (the current in R1). This is calculated as V/R1 where V is the applied voltage of 85 V
i1 = 85 / 35 = 2.43 A. 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: - 2.43 A
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 85 V. 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.
6) The initial rate of change of current is calculated as dI/dt = V/L = 85 / 50 = 1.7 A/s
7) I have assumed that L has no resistance, so after a long period of time there will be no voltage developed across L; the entire supply voltage will appear across R2.