In the circuit diagram below, resistor R, with a resistance of 5.6 Ω, is connected, together with a switch, an ammeter and a high-resistance voltmeter, to a battery with an unknown internal resistance, r. The resistance of the connecting wires and the ammeter may be ignored. The graph below shows the potential difference across the terminals of the battery as a function of time. At time t₁, switch S is closed. 8.1 Define the term emf of a battery. 8.2 Write down the value of the emf of the battery. 8.3 When switch S is CLOSED, calculate the: 8.3.1 Current through resistor R 8.3.2 Power dissipated in resistor R 8.3.3 Internal resistance, r, of the battery. 8.4 Two IDENTICAL resistors, each with resistance X, are now connected in the same circuit with switch S closed, as shown below. The ammeter reading now increases to 4 A. 8.4.1 How would the voltmeter reading change? Choose from INCREASES, DECREASES or REMAINS THE SAME. 8.4.2 Calculate resistance X.

NSC Physical Sciences Electric Circuits: In the circuit diagram below, re

In the circuit diagram below, resistor R, with a resistance of 5.6 Ω, is connected, together with a switch, an ammeter and a high-resistance voltmeter, to a battery with an unknown internal resistance, r - NSC Physical Sciences - Question 8 - 2019 - Paper 1

Question 8

In the circuit diagram below, resistor R, with a resistance of 5.6 Ω, is connected, together with a switch, an ammeter and a high-resistance voltmeter, to a battery ... show full transcript

Worked Solution & Example Answer:In the circuit diagram below, resistor R, with a resistance of 5.6 Ω, is connected, together with a switch, an ammeter and a high-resistance voltmeter, to a battery with an unknown internal resistance, r - NSC Physical Sciences - Question 8 - 2019 - Paper 1

Step 1

Define the term emf of a battery.

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Answer

The emf (electromotive force) of a battery is defined as the maximum potential difference provided by the battery when no current is flowing. It represents the energy supplied by the battery per coulomb of charge passing through it.

Step 2

Write down the value of the emf of the battery.

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Answer

The value of the emf of the battery is 13 V.

Step 3

When switch S is CLOSED, calculate the current through resistor R.

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Answer

Using Ohm's Law, we can determine the current (I) through resistor R:

$I = \frac{V}{R} = \frac{10.5 V}{5.6 \Omega} \approx 1.88 A$

Step 4

When switch S is CLOSED, calculate the power dissipated in resistor R.

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The power (P) dissipated in resistor R can be calculated using the formula:

$P = I^2 R = (1.88 A)^2 \times 5.6 \Omega \approx 19.688 W$

Step 5

When switch S is CLOSED, calculate the internal resistance, r, of the battery.

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Answer

We can establish the relationship between voltage, current, and internal resistance:

$\varepsilon = I(R + r)\n13 = 1.88(5.6 + r)\nSolving for r, we find r \approx 1.31 \Omega.$

Hence, the internal resistance of the battery is approximately 1.31 Ω.

Step 6

How would the voltmeter reading change? Choose from INCREASES, DECREASES or REMAINS THE SAME.

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Answer

The voltmeter reading would DECREASE.

Step 7

Calculate resistance X.

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Answer

Using the circuit with two identical resistors:

For two resistors in parallel:

\nUsing Ohm's law: $$I = \frac{V}{R_{total}};\n\n4 A = \frac{13 V}{2.8 \Omega}\n\nTherefore, X \approx 1.49 \Omega.$$

In the circuit diagram below, resistor R, with a resistance of 5.6 Ω, is connected, together with a switch, an ammeter and a high-resistance voltmeter, to a battery with an unknown internal resistance, r - NSC Physical Sciences - Question 8 - 2019 - Paper 1

Worked Solution & Example Answer:In the circuit diagram below, resistor R, with a resistance of 5.6 Ω, is connected, together with a switch, an ammeter and a high-resistance voltmeter, to a battery with an unknown internal resistance, r - NSC Physical Sciences - Question 8 - 2019 - Paper 1

Define the term emf of a battery.

Write down the value of the emf of the battery.

When switch S is CLOSED, calculate the current through resistor R.

When switch S is CLOSED, calculate the power dissipated in resistor R.

When switch S is CLOSED, calculate the internal resistance, r, of the battery.

How would the voltmeter reading change? Choose from INCREASES, DECREASES or REMAINS THE SAME.

Calculate resistance X.

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