Parallel Circuit Analysis

00:00 6 marks

7. A resistor \(R_1\) of resistance 6.0 \(\Omega\) and a resistor \(R_2\) of resistance 12.0 \(\Omega\) are connected in parallel to a 9.0 V battery of negligible internal resistance.

(a) Examine and interpret the provided circuit diagram to explain how the 9.0 V battery is connected to two parallel resistor branches. [1]

(b) Calculate the total resistance of the parallel combination. [2]

(d) Calculate the power dissipated in resistor \(R_1\). [2]

Part a

2 minutes 1 marks

Question

Examine and interpret the provided circuit diagram to explain how the 9.0 V battery is connected to two parallel resistor branches. [1]

Hint Hint

Hint

Observe the battery and the arrangement of the two parallel resistor branches. Note the labels indicating R₁ and R₂.

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Complete Answer

The provided diagram clearly indicates that a 9.0 V battery is connected to two parallel branches. One branch includes a resistor labeled R₁ = 6.0 Ω and the other branch includes a resistor labeled R₂ = 12.0 Ω.

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Part b

3 minutes 2 marks

Question

Calculate the total resistance of the parallel combination. [2]

Hint Hint

Hint

Use the formula \(1/R_p = 1/R_1 + 1/R_2\).

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4.0 Ω

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Part c

2 minutes 1 marks

Question

Calculate the total current supplied by the battery. [1]

Hint Hint

Hint

Use Ohm’s Law: \(I = V/R_p\).

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2.25 A

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Part d

2 minutes 2 marks

Question

Calculate the power dissipated in resistor \(R_1\). [2]

Hint Hint

Hint

Remember the formula \(P = V^2/R\) and use the battery voltage for \(R_1\).

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13.5 W

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