circuit physics?

Question

Two resistors A and B are connected in parallel across a 6 V battery. The current throught B is found to be 2 A. When the two resistors are connected in series to the 6 V battery, a voltmeter connected across resistor A measures a voltage of 2 V. Find the resistance of A in units of ohms.

Any help is appreciated. I have a test tomorrow and this is on the review guide and I can't get it. Thank you.

Answer 1

V=IRb ==>Rb=v/I=6/2=4 ohms| because the voltage is the same across both and we know the current through B, we can find it's resistance

The same current flows through both resistors: We now the voltage across Rb (because the total voltage is 6, the voltage drop across Ra is 2, Rb has to be 4) and we now using the resistance we just found, we can find the loop current, 6/4 =1.5 A

So we know the current and the voltage, we can find Ra: 2/1.5 or 1.33 ohms.

Answer 2

Since b has a current of 2A thru it with 6V across it, it has a resistance of
B = 6/2 = 3 ohms
In series, if there's 2 volts across A, then there is 4 volts across B and the current thru the circuit is
I = 4/3 A so that the resistance of A is
2/(4/3) = 3/2 or 1.5 ohms

HTH ☺

Doug