What is the potential difference between points P and Q?

Understand the Problem

The question is asking for the potential difference between points P and Q in a circuit with three batteries and three identical resistors. It involves calculating the total voltage influenced by the arrangement and values of the batteries.

Answer

$7.5 \, \text{V}$

Steps to Solve

Identify the Voltage Contributions The circuit has three batteries connected, providing voltages: 9.6 V, 8.4 V, and 6.3 V. The battery orientation influences the potential difference across P and Q.
Calculate Total Voltage Drop We will compute the total voltage created by the three batteries from P to Q. The direction from P to Q goes through the 9.6 V and the 6.3 V battery, but opposes the 8.4 V battery. Thus, the effective voltage is: $$ V = 9.6 , \text{V} + 6.3 , \text{V} - 8.4 , \text{V} $$
Perform the Calculation Continuing from the previous step, calculate: $$ V = 9.6 + 6.3 - 8.4 = 7.5 , \text{V} $$
Determine the Potential Difference Since the question requires the potential difference between points P and Q, we regard the effective voltage calculated above.
Select the Closest Answer Option Given that we computed the potential difference as 7.5 V, we will choose the closest option from the provided answers.

The potential difference between points P and Q is $7.5 , \text{V}$.

More Information

The potential difference is essentially the net voltage taking into account the direction of batteries in the circuit. It shows how the arrangement affects voltage distribution, which is crucial in electrical circuits.

Tips

Neglecting Battery Orientation: Failing to account for the direction of the batteries can lead to incorrect voltage addition or subtraction.
Miscalculating Total Voltage: Simple arithmetic errors can easily change the final result, so careful calculations are necessary.

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