Consider the three circuits shown above. All the resistors and all the batteries

Question

Consider the three circuits shown above. All the resistors and all the batteries are identical. Select true or false for each statement. The current through a resistor is the same in circuits A and B. The power dissipated in circuit A is twice the power dissipated in circuit B. The current through a resistor is the same in circuits A and C. The total power dissipated in circuit C is twice the total power dissipated in circuit B. The voltage across a single resistor in circuit C is twice the voltage across a single resistor in circuit B.

Explanation / Answer

1. False

Current through A:

I = V/Req = V/R

Current through B:

I = V/Req = V/2R

2. True

Power in A

P = V^2/Req = V^2/R

Power in B:

P = V^2/Req = V^2/2R

3. True

Current through A:

I = V/R

Current through C:

Req = R*R/(R+R) = R/2

I = V/Req = 2V/R

Current in C through each resistor is half of total current = V/R

4. False

Power in B = V^2/2R

Power in C = V^2/(R/2) = 2*V^2/R

5. True

Voltage through each resistor in B = (V/2R)*R = V/2

Voltage through each resistor in C = V, Because in parallel combination voltage remains same in each resistor.

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