Circuits and resistances...?

Question

Two resistors, A and B, are connected in parallel across a 6.0-V battery. The current through B is found to be 2.0 A. When the resistors are connected in series to the 6.0-V battery, a voltmeter connected across resistor A measures a voltage of 4.0 V. Find the resistance of A.

Answer 1

First find the resistance of B:

V = IR

6 = 2Rb

Rb = 6/2 = 3Ω

Now, in series A and B are a voltage divider.

Va = Vt* Ra/(Ra + Rb)

4 = 6 * Ra/(Ra + 3)

4(Ra+3) = 6Ra

4Ra + 12 = 6Ra

12 = 2Ra

6Ω = Ra