Time constant

[Andrew187]

Hi folks I was wondering if someone can help me with some revision questions, that I need the answer and the exponential formulas, it would be a great help. My exams in a couple of weeks and I really needed to learn this stuff.

1. A coil of inductance 4H and resistance of 80Ω is connected in parallel with a 200Ω of resistor of negligible inductance across a 200v dc supply. The switch connecting these to the supply is then opened; the coil and resistor remain connected together. State in each case one for immediately before and one for immediately after opening the switch;

a) The current Through the resistor
b) The current through the coil
c) The e.m.f induced in the coil
d) The voltage across the coil

[rievax_60]

Re: Time constant

The current through the coil will settle to 200v/80Ω = 2.5A, while the switch is closed.
The coil's inductance will maintain the same 2.5A current flow immediately after the switch is opened. This 2.5A current will flow through the coil's inductance, the coil's 80Ω internal resistance and the 200Ω resistor as one circuit.
The voltage across the 200Ω resistor will be 2.5A x 200Ω = 500V.

[Andrew187]

Re: Time constant

Would you say this is correct then and the formulas and the units of calculation??

A coil of inductance 4H and resistance of 80Ω is connected in parallel with a 200Ω of resistor of negligible inductance across a 200v dc supply. The switch connecting these to the supply is then opened; the coil and resistor remain connected together. State in each case one for immediately before and one for immediately after opening the switch;

The current Through the resistor

Switch closed
200v/200Ω =1a
Switch open
200v/80Ω =2.5a

The current through the coil

Switch Closed
200v/80Ω = 2.5a
Switch open
200v/80Ω = 2.5a


The e.m.f induced in the coil

Switch closed
(2.5a*80Ω)/200v = 0v
Switch Open
2.5a *(200Ω + 80Ω) = 700v

The voltage across the coil

Switch closed
200v/1a = 200v
Switch open
2.5a * 200Ω = 500v

[rievax_60]

Re: Time constant

All looks right except for the e.m.f. induced in the coil. It will be zero because there is no change in current over time while the switch has been closed for long enough but I don't how to show a formula.

[rievax_60]

Re: Time constant

Maybe this http://www.allaboutcircuits.com/vol_1/chpt_15/2.html

[rievax_60]

Re: Time constant

change in current, di = 0
0/dt = 0
L x 0 = 0V