Two resistors, A and B, are connected in parallel across a 8.0 V battery. The current through B is found to be 3.0 A. When the two resistors are connected in series to the 8.0 V battery, a voltmeter connected across resistor A measures a voltage of 2.4 V. Find the resistances A and B.

R_A = 2.67 ohms

R_B = 1.14 ohms

Explanation:

When the resistors are connected in parallel, the voltage will be the same across both resistors A and B.

Thus, we now have the current and the voltage across B and so we can use Ohm's Law to find the resistance.

V/I = R

Thus, resistance of B; R_B = 8/3

R_B = 2.67 ohms

Now, when the resistors are connected in series, the voltage drop across B is;

V = 8V - 2.4V = 5.6V

Since we now have the resistance of B, we can find the current using Ohm's Law. Thus;

I = V/R

I = 5.6/2.67

I = 2.1 A

Now, current is the same for all resistances in a series circuit because this is the same current through resistors A and B. So, we can use Ohm's law again to find the resistance across A.

So, R = V/I

R_A = 2.4/2.1

R_A = 1.14 ohms