A resistor R₁ of resistance 6.0 Ω and a resistor R₂ of resistance 12.0 Ω are connected in parallel. This combination is connected in series with a resistor R₃ of resistance 4.0 Ω and a cell of emf 9.0 V and negligible internal resistance. The configuration is illustrated in the provided diagram in Part (a).
(b) Calculate the total resistance of the circuit. [3]
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(c) Calculate the current flowing through resistor R₃. [1]
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(d) Calculate the power dissipated in resistor R₁. [3]
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Question
The provided diagram below illustrates the circuit configuration for this arrangement. Interpret this diagram to understand how the components are connected for the subsequent calculations. [0]
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Observe the connections in the provided diagram. Identify which components are in series and which are in parallel. Note the labeled values for the emf and resistances.
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Not applicable (Diagram provided).
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Question
Calculate the total resistance of the circuit. [3]
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First, find the equivalent resistance (Rp) of the parallel combination of R₁ and R₂ using the formula 1/Rp = 1/R₁ + 1/R₂. Then, add this equivalent resistance to the resistance of R₃ (which is in series) to find the total resistance.
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Question
Calculate the current flowing through resistor R₃. [1]
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Resistor R₃ is located in the main part of the circuit (as interpreted from the diagram), in series with both the cell and the parallel combination. Therefore, the current through it is equal to the total current. Use Ohm’s law (I = V/R) with the cell’s emf and the total resistance found in part (b).
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1.1 A (or 1.125 A)
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Question
Calculate the power dissipated in resistor R₁. [3]
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To determine the power in R₁, first find the voltage across R₁ (by interpreting the voltage across the parallel section from the diagram) or the current through it. Knowing that R₁ is in parallel with R₂, its voltage is the same as that across the parallel branch. Use P₁ = V₁²/R₁ (with V₁ equal to the voltage across the parallel section). Alternatively, you may calculate the current through R₁ and then use P₁ = I₁²R₁.
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3.4 W (or 3.375 W)
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