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 two 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 resistances of A and B

Answer 1

The resistance of A is 6 ohms and the resistance of B is 3 ohms

Step-by-step explanation:

Step 1: For the first connection (parallel connection), the resistance of B will be calculated.

Note: in a parallel connection, the voltage through each resistor is the same.

`V = I_AR_A = I_BR_B\\\\R_B = (V)/(I_B) = (6)/(2) = 3 \ ohms`

Step 2: The resistance of A will be calculated from the second connection (series connection)

Note: in series connection, the current flowing in each resistor is the same

`V = V_A + V_B\\\\V = IR_A + IR_B\\\\The \ voltage \ drop \ in \ B; \ V_B = V- V_A\\\\V_B = 6 - 4 = 2 \ V\\\\IR_B = 2\ V\\\\I = (2 \ V)/(R_B)= (2)/(3) \ A\\\\The \ resistance \ of \ A \ is \ calculated \ as ;\\\\IR_A = 4 \ V\\\\R_A = (4)/(I) = (4 * 3)/(2) = 6 \ ohms`