OCR · A-Level · Physics
Course version: H556 · Version from Sept 2015
(d) total resistance of two or more resistors in parallel; 1/R = 1/R₁ +…
Full specification wording
Series and parallel circuits: (d) total resistance of two or more resistors in parallel; 1/R = 1/R₁ + 1/R₂ + ...
For resistors connected in parallel, the reciprocal of the total resistance equals the sum of the reciprocals of individual resistances: 1/R = 1/R₁ + 1/R₂ + ... .
Checked against the OCR H556 specification (opens in a new tab) on .
- Point 4 of 6
Study notes
From the checked teaching notes for this specification point.
The idea
For resistors connected in parallel, the reciprocal of the total resistance equals the sum of the reciprocals of individual resistances: 1/R = 1/R₁ + 1/R₂ + ... . This is because the potential difference across each resistor is the same, and the total current is the sum of the currents through each resistor. For example, two 10 Ω resistors in parallel give 1/R = 1/10 + 1/10 = 2/10, so R = 5 Ω. The total resistance is always less than the smallest individual resistance. In multiple-choice questions, you may need to calculate total resistance or identify the correct formula. Remember to take the reciprocal of the sum to find R.
What earns the marks
- Total resistance in parallel is given by 1/R = 1/R₁ + 1/R₂ + ... .
- The potential difference across each resistor in parallel is the same.
- The total current is the sum of the currents through each resistor.
- The total resistance is always less than the smallest individual resistance.
- Application: calculate total resistance for two or more resistors in parallel.
Common mistakes and how to put them right
Misunderstanding: total resistance in parallel is the sum of individual resistances.
Put it right: It is the reciprocal of the sum of reciprocals.
Misunderstanding: total resistance in parallel is greater than the largest resistance.
Put it right: It is always less than the smallest individual resistance.
Misunderstanding: forgetting to take the reciprocal of the sum to find R.
Put it right: After summing reciprocals, invert the result to get R.
Misunderstanding: voltage is different across each resistor in parallel.
Put it right: Voltage is the same across all parallel branches.
Exam tips
- In multiple-choice questions, if resistors are connected between the same two points, they are in parallel; use the reciprocal formula.
- For two resistors in parallel, you can use the product-over-sum shortcut: R = (R₁ × R₂)/(R₁ + R₂).
- Always check that your calculated total resistance is less than the smallest individual resistance.
Try the lesson
The start of the Series and parallel circuits: (d) total resistance of two or more resistors in parallel; 1/R = 1/R₁ + 1/R₂ + ... lesson, made from checked teaching notes for this specification point.
Listen
For resistors connected in parallel, the reciprocal of the total resistance equals the sum of the reciprocals of individual resistances: 1/R = 1/R₁ + 1/R₂ + ... This is because the potential difference across each resistor is the same, and the total current is the sum of the currents through each resistor. For example, two 10 Ω resistors in parallel give 1/R = 1/10 + 1/10 = 2/10, so R = 5 Ω. The total resistance is always less than the smallest individual resistance. In multiple-choice questions, you may need to calculate total resistance or identify the correct formula. Remember to take the reciprocal of the sum to find R. A strong answer earns marks for these points. Total resistance in parallel is given by 1/R = 1/R₁ + 1/R₂ + ... The potential difference across each resistor in parallel is the same. The total current is the sum of the currents through each resistor. The total resistance is always less than the smallest individual resistance. A common slip: Misunderstanding: total resistance in parallel is the sum of individual resistances. Instead, it is the reciprocal of the sum of reciprocals. Exam tip: In multiple-choice questions, if resistors are connected between the same two points, they are in parallel; use the reciprocal formula.
See it
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