A battery has an EMF of 12 V and internal resistance r. The battery is connected in a circuit as shown. (a) The reading on the ammeter is 0.38 A. (i) Determine the terminal potential difference (t.p.d.) of the battery. (ii) Calculate the internal resistance r of the battery. (iii) Calculate the power dissipated by the internal resistance of the battery. (b) The circuit is now rearranged as shown. State whether the power dissipated by the internal resistance of the battery is greater than, equal to, or less than the value determined in (a)(iii). You must justify your answer.

Scottish Highers Physics Internal Resistance: A battery has an EMF of 12 V and

A battery has an EMF of 12 V and internal resistance r - Scottish Highers Physics - Question 12 - 2023

Question 12

A battery has an EMF of 12 V and internal resistance r. The battery is connected in a circuit as shown. (a) The reading on the ammeter is 0.38 A. (i) Determine the... show full transcript

Worked Solution & Example Answer:A battery has an EMF of 12 V and internal resistance r - Scottish Highers Physics - Question 12 - 2023

Step 1

Determine the terminal potential difference (t.p.d.) of the battery.

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Answer

To find the terminal potential difference (V), we use the formula:

V = E - I imes r

Where:

E = EMF of the battery = 12 V
I = current = 0.38 A
r = internal resistance (which we will calculate later)

First, we calculate the total resistance in the circuit. The total resistance (R) in the circuit is:

R = R_1 + R_2 = 16 \, \Omega + 16 \, \Omega = 32 \, \Omega

Using Ohm's law:

I = \frac{E}{R + r} \Rightarrow r = \frac{E}{I} - R

So:

V = I imes R = 0.38 imes 24 = 9.1 \, V

Step 2

Calculate the internal resistance r of the battery.

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Answer

Using the earlier relationship,

12 = 0.38 imes (24 + r)

Expanding this, we have:

12 = 9.12 + 0.38r

Rearranging to isolate r gives:

0.38r = 12 - 9.12 = 2.88

So:

r = \frac{2.88}{0.38} \approx 7.6 \, \Omega

Step 3

Calculate the power dissipated by the internal resistance of the battery.

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Answer

The power (P) dissipated by the internal resistance can be calculated using:

P = I^2 r

Substituting the values:

P = (0.38)^2 \times 7.6 = 1.1 \, W

Step 4

State whether the power dissipated by the internal resistance of the battery is greater than, equal to, or less than the value determined in (a)(iii).

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Answer

The power dissipated will be less than the previous value determined, given that:

The total circuit resistance increases,
Current decreases,
Internal resistance stays the same.

Thus, if the internal resistance remains unchanged and the overall resistance in the circuit increases, the current through the internal resistance decreases, resulting in less power dissipation.

A battery has an EMF of 12 V and internal resistance r - Scottish Highers Physics - Question 12 - 2023

Worked Solution & Example Answer:A battery has an EMF of 12 V and internal resistance r - Scottish Highers Physics - Question 12 - 2023

Determine the terminal potential difference (t.p.d.) of the battery.

Calculate the internal resistance r of the battery.

Calculate the power dissipated by the internal resistance of the battery.

State whether the power dissipated by the internal resistance of the battery is greater than, equal to, or less than the value determined in (a)(iii).

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