Help in Finding the v(t) of the RC circuit?

[ichilouch]

Homework Statement

This is the Problem with the answer:

Homework Equations

V=RI
V_{c}(t)=V_{0}e^{-t/(RC)}

The Attempt at a Solution

Actually, this is a topic about laplace transform.
I tried to solve the problem using the formula.

@t<0
I=40/(3+8) = 40/11 A
V @ 3 ohms = 40/11 * 3 = 120/11 V

@t=0 <switch is opened>
hence: v(t) = (120/11) e^{-t/(8*(1/10))}

v(t) = (120/11) e^{(-5t/4)}

 

[vanhees71]

The answer is evidently not entirely correct, because there appears a dimensionful quantity in the argument of the exponential function!

 

[ichilouch]

The answer is evidently not entirely correct, because there appears a dimensionful quantity in the argument of the exponential function!

How do you solve this?

 

[rude man]

The given answer is wrong, both in initial voltage and in the time constant.

At least in your answer the time constant is correct.

 

[gneill]

1. The given solution does not match the given circuit. Perhaps the circuit diagram was altered at some point to make it a "new problem" but the solution was not changed accordingly (the general form of the solution might be correct but the constants don't match the circuit diagram as given).

2. Regarding Vahees71's observation about the units in the exponential function, this is another indication of a lack of care by the publisher of the problem. Although occasionally one may come across examples of formulae that are presented with numerical constants where units are to be assumed but are not shown for esthetic or pedagogical reasons for a well informed audience, it is really not appropriate for introductory course material such as this.

Note also that the problem statement does not define what V(t) is. Between what points in the circuit is it defined? It should be clearly specified on the circuit diagram or in the problem text!

I'd be curious to know the source of the problem statement. It is disturbing to see learning material that is this shoddy being given to students.

@ichilouch: you seem to have assumed in your solution attempt that V(t) is the voltage across the 3 Ohm resistor, but that doesn't seem right given the the proposed form of the solution. Once the switch opens the potential across the 3 Ohm resistor would be zero since no current can flow through an open circuit.

You should determine what the definition of V(t) is and determine its initial value prior to the switch commutation. (Presumably they are really looking for the potential across the 8 Ohm resistor and its parallel capacitor, but without it actually being specified in the problem statement it's just an assumption open to interpretation. Not a good thing for assigned material to be marked!)

If this problem is to be solved via Laplace transforms as you state in your first post then I would expect your solution to involve the Laplace Domain version of a circuit equation with the time domain solution emerging from the inverse transform. Alternatively you would have to first write the differential equation for the desired voltage and then use Laplace transform methods on that.

3. This problem belongs in either Introductory Physics or Engineering, Comp Sci & Technology forums, not Advanced Physics. I will move the thread to CS&T.