RL Circuit Analysis: Comparing Resistor and Coil Voltages

[member 392791]

Homework Statement

At the moment t = 0, a 24.0-V battery is connected
to a 5.00-mH coil and a 6.00-V resistor. (a) Immediately
thereafter, how does the potential difference across the
resistor compare to the emf across the coil? (b) Answer
the same question about the circuit several seconds later.
(c) Is there an instant at which these two voltages are equal
in magnitude? If so, when? Is there more than one such
instant? (d) After a 4.00-A current is established in the
resistor and coil, the battery is suddenly replaced by a short
circuit. Answer parts (a), (b), and (c) again with reference
to this new circuit.

Homework Equations

The Attempt at a Solution

a) V_r = 0 at t=0
b) V_r = ε at t --> ∞

V_l = V_r at t=??

I tried doing -L di/dt = IR to solve for t and it got me nowhere

d) when the battery is removed,
I got V_r = ε at t=0 and V_r = 0 at t-->∞
, and still don't know if there is a time that V_r = V_l

 

[NascentOxygen]

The elements are in series, presumably.

I tried doing -L di/dt = IR to solve for t and it got me nowhere

If you can't solve a first-order differential equation, then steal someone else's solution from a textbook. The response of a first order system (whether R+L or R+C ) is something you need to practise until you can sketch the graph in your sleep.

 

[member 392791]

I know how to do the differential equation

the problem is that everything canceled out and got me back to R = R.

 

[NascentOxygen]

What is the general solution to the DE with L, R and V?