Solving Circuit Resistor Equations: Current, Voltage, Power

[sonutulsiani]

Homework Statement

Find current flowing through each resister, voltage across each resister and power consumed by each element in the following circuit.

See the attachment

Homework Equations

The Attempt at a Solution

The question I want to ask here is that is the current = 10 A? Because I got 2 answers for current, 0 A and 10 A.

I did this:

I combined 10 and 10 ohm resistors to get a 5 ohm resistor.
Now total power consumed=total power supplied

So I^2(3) + I^2(5) + I^2(2) = 100I
which gives I = 0 or 10. Which one should I take?

 

[berkeman]

Homework Statement

Find current flowing through each resister, voltage across each resister and power consumed by each element in the following circuit.

See the attachment

Homework Equations

The Attempt at a Solution

The question I want to ask here is that is the current = 10 A? Because I got 2 answers for current, 0 A and 10 A.

I did this:

I combined 10 and 10 ohm resistors to get a 5 ohm resistor.
Now total power consumed=total power supplied

So I^2(3) + I^2(5) + I^2(2) = 100I
which gives I = 0 or 10. Which one should I take?

I=0 is called the degenerate solution, and is not physical in this case. Use I=10.

 

[sonutulsiani]

Ok but what is the reason again? What is degenerate solution ?

 

[vk6kro]

If you add up the resistor values, you can get the total current flowing because you know the supply voltage.

Then take this current and work out the voltage across each resistor and the power dissipated in it.

With this circuit, you can tell by looking at it that zero current is not an option.

 

[berkeman]

Ok but what is the reason again? What is degenerate solution ?

I apologize if I'm using and incorrect term there. I've been googling for a bit trying to find you a good definition, with very little luck so far. By degenerate solution, I meant when the variable x = 0 is a solution to an equation f(x) = 0, and it is a solution because all terms in the equation are zero. It's like multiplying both side of any equation by zero, and saying, yes, both sides are equal now.

In your equation you had I on one side and all I^2 on the other. You should divide by I in that case, before solving the equation. If you do that, you will not end up with I=0 as a degenerate solution of the equation.