# Kirchhoff's laws circuit, How to calculate unknown resistor?

First time here! I got a question on a test that I cant get my head around. • How do I calculate value of R2 ?
• Is it possible ?

Thanks in advance !

• There's a built-in schematic editor on this site, if you want to make your schematic look nicer. – Hearth Mar 12 at 15:26
• Yes it's possible. You have three equations and constraints. HINT: Solve for the power dissipation of R2 in terms of I. Another hint: R2 is between 50 and 100 ohms, and the loop current is less than 250mA – BB ON Mar 12 at 15:35
• Thanks! I think i got it now! – Simon Watti Mar 12 at 16:03

## 1 Answer

Express the current through the circuit in function of R2:

$$I = \frac{10 V}{R_2 + 15 \Omega}$$

Express power dissipated in the second resistor in function of the current and resistance:

$$1W = P = I^2R_2 = \biggl(\frac{10 V}{R_2 + 15 \Omega}\biggl)^2 \times\ R_2$$

Solve for resistance, solve for current, solve for other resistance's dissipated power.