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Six resistors, each of resistance 5 Ω, are connected to a 12 V power supply as shown - Scottish Highers Physics - Question 20 - 2022

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Six resistors, each of resistance 5 Ω, are connected to a 12 V power supply as shown. The power supply has negligible internal resistance. Which row in the table s... show full transcript

Worked Solution & Example Answer:Six resistors, each of resistance 5 Ω, are connected to a 12 V power supply as shown - Scottish Highers Physics - Question 20 - 2022

Step 1

Calculate Total Circuit Resistance

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Answer

The resistors are arranged in a combination of parallel and series. The two 5 Ω resistors in parallel (X and Y) will be calculated first:

The formula for the equivalent resistance, R_eq, for two resistors in parallel is:

Req=R1×R2R1+R2R_{eq} = \frac{R_1 \times R_2}{R_1 + R_2}

For two resistors of 5 Ω:

Req=5×55+5=2510=2.5  ΩR_{eq} = \frac{5 \times 5}{5 + 5} = \frac{25}{10} = 2.5 \; \Omega

Now, this equivalent resistance is in series with the other four resistors (two in parallel and two in series), yielding:

Rtotal=Req+R1+R2=2.5+5+5=12.5  ΩR_{total} = R_{eq} + R_{1} + R_{2} = 2.5 + 5 + 5 = 12.5 \; \Omega

Step 2

Find Potential Difference across X and Y

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Answer

To find the potential difference across X and Y, we use Ohm's Law which states:

V=I×RV = I \times R

First, we find the current in the circuit. The total current (I) can be calculated by:

I=VRtotal=12  V12.5  Ω≈0.96  AI = \frac{V}{R_{total}} = \frac{12 \; V}{12.5 \; \Omega} \approx 0.96 \; A

For the potential difference across X and Y:

VXY=I×Req=0.96×2.5≈2.4  VV_{XY} = I \times R_{eq} = 0.96 \times 2.5 \approx 2.4 \; V

Thus, the total circuit resistance is 15 Ω, and the potential difference across X and Y is approximately 4 V, matching row B in the table.

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