Show that the voltage across resistor R2

[KillerZ]

Homework Statement

In the circuit shown, the same current must flow through all three componets as a result of conservation laws. Using the fact that the total power supplied equal the total power absorbed, show that the voltage across resistor R₂ is given by:

$$v_{R_{2}} = v_{s}\frac{R_{2}}{R_{1} + R_{2}}$$

Homework Equations

$$p = vi = i^{2}R = \frac{v^{2}}{R}$$

The Attempt at a Solution

I said:

$$p_{v_{s}} = p_{R_{1}} + p_{R_{2}}$$

because power supplied = power absorbed

$$p_{v_{s}} = p_{R_{1}} + p_{R_{2}}$$

But I don't think this is right because it would not simplify right.

$$v_{s}i = i^{2}R_{1} + \frac{v_{R_{2}}^{2}}{R_{2}}$$

 

[rl.bhat]

Since total power supplied is equal to the total power absorbed, there is no internal resistance in Vs.
Apply the ohm's law to the circuit and find VR2.

 

[KillerZ]

I am still having trouble with this.

I know Ohm's law is

$$v = IR$$

$$I = \frac{v}{R}$$

and

$$R = \frac{v}{I}$$

but do I just just use them with this:

$$p_{v_{s}} = p_{R_{1}} + p_{R_{2}}$$

$$v_{s}i = i^{2}R_{1} + \frac{v_{R_{2}}^{2}}{R_{2}}$$

 

[rl.bhat]

What is the total resistance in the circuit?
What is the current in the circuit?
And then what is the voltage across R2?
Here you need not use the power formula.
In the problem the mention of the power is to emphasis the absence of internal resistance in the source.