When switch is on, the voltage is being calculated as $45V$. What is the voltage when switch is off?

Question

When switch is off, the voltage is being calculated as $45V$. What is the voltage when switch is on?

I'm stuck at this problem!

Regards,

Answer 1

Well, when the switch is open we can write:

$$\epsilon+\text{V}_{3\space\Omega}=45\tag1$$

Now, when we switch is closed:

$$\text{I}_{\space\text{in}}=\frac{\text{V}_{\space\text{in}}}{\text{R}_{\space\text{in}}}=\frac{45}{15}=3\tag2$$

So:

$$\text{V}_{\space\text{measured}}=\Delta\text{V}=\left(\epsilon+\text{V}_{3\space\Omega}\right)_{\space\text{open switch}}-\left(\text{I}_{\space\text{in}}\cdot3\space\Omega\right)=45-3\cdot3=36\tag3$$