Lesson summary
10.2.4 Resistors in Parallel — AS PHYSICS 9702 notes: Derive and use 1/R = 1/R₁ + 1/R₂ + … for resistors in parallel.Current — it splits at the junction and is shared between the resistors.Potential difference — it is the same across all the resistors.Combined resistance — the re…
- What the symbols mean
- Smaller total
- Two equal resistors
- Reciprocal
- Final step
- Common mistake
Section 1 of 7Parallel circuit rules
Current
- Current it splits at the junction and is shared between the resistors.
Potential difference
- Potential difference it is the same across all the resistors.
Combined resistance
- Combined resistance the reciprocal of the combined resistance is the sum of the reciprocals of the individual resistances.
Section 2 of 7Derivation from Kirchhoff’s laws
1
The same p.d. V is across each resistor.
2
By Kirchhoff’s first law, the total current is I = I1 + I2.
3
Using I = V/R for each, V/R = V/R1 + V/R2.
4
Dividing by V gives 1/R = 1/R1 + 1/R2.
Section 3 of 7The equation
Equation
- 1/R = 1/R1 + 1/R2 + 1/R3 + …What the symbols mean: RT = total resistance of resistors in parallel (Ω), always smaller than the smallest one · R1, R2 = the separate resistances (Ω)
Smaller total
- Smaller total the combined resistance decreases and is less than the resistance of any individual component.
Two equal resistors
- Two equal resistors the combined resistance is halved.
Section 4 of 7Using reciprocals
1Reciprocal
- Reciprocal the reciprocal of a value is 1/value.
2Fractions
- Fractions if the number is already a fraction, flip the numerator and denominator.
3Final step
- Final step after adding the reciprocals, calculate 1/answer to find R, using the x−1 button on a calculator.
4Common mistake
- Common mistake leaving the answer as 1/RT.
Section 5 of 7More from the specification
1Solving network circuit problems
- Solving network circuit problems applying Kirchhoff's laws around closed circuit loops allows systematic analysis of branched parallel and series resistor combinations.
2Power delivered by dc supplies
- Power delivered by dc supplies electrical power delivered by a power supply to connected parallel loads equals terminal voltage multiplied by total current.
3Energy conservation in closed loops
- Energy conservation in closed loops around any closed electrical circuit loop, total energy supplied by EMF sources equals total energy dissipated.
4Equivalent Resistance in Parallel Circuits
- When multiple resistors are connected in parallel across an electrical circuit, the reciprocal of the total equivalent resistance is equal to the sum of individual reciprocals: 1 / Rtotal = 1 / R1 + 1 / R2 + 1 / R3.
5Kirchhoff's Laws for Circuit Analysis
- In solving electrical network problems, Kirchhoff's first law reflects charge conservation,
- (sum of currents entering a junction equals sum leaving)
- while Kirchhoff's second law reflects energy conservation around any closed circuit loop.
- (sum of EMFs equals sum of IR drops)
6Resistors Connected in Series
- For resistors connected in series, the same continuous electric current passes through each component and total circuit resistance is the arithmetic sum: Rtotal = R1 + R2 + R3.What the symbols mean: RT = total resistance of resistors in series (Ω) · R1, R2 = the separate resistances (Ω)
7Power Output from Electrical Supply
- The total electrical power delivered by a DC power supply to a connected network is given by P = VI,
- where V is terminal voltage and I is total current supplied to the load.
8Charge
- Quantity of electricity in coulombs, Q = It.What the symbols mean: Q = charge (C) · I = current (A) · t = time (s)
9Branch
- Path connecting two junctions.
10Series circuit
- Circuit with components connected one after another in a single loop.
11Parallel circuit
- Circuit with branches; same p.d. across each branch.
12Closed circuit
- Complete loop with a source in which current can flow
13Energy transferred
- W = V Q, in joules.What the symbols mean: E or W = energy transferred (J) · Q = charge (C) · V = potential difference (V) · I = current (A) · t = time (s)
14Series
- Components in one loop, sharing the e.m.f. between them.
15Ammeter
- Component that measures current.
16Voltmeter
- Instrument that measures p.d., connected in parallel.
Section 6 of 7Key terms
| Term | Meaning |
|---|---|
| Parallel circuit | Components connected across the same two points so each has the same p.d. |
| Reciprocal | The value 1 divided by a number. |
| Combined resistance | Single resistance that could replace the network and draw the same current. |
| Kirchhoff’s first law | Sum of currents into a junction equals the sum out. |
Section 7 of 7Exam technique
1
Leaving the answer as 1/RT — take the reciprocal to find RT.
2
Adding the resistances directly for resistors in parallel.
3
Expecting the total to be larger than the smallest resistor — it is smaller.
4
Thinking the current is the same in each branch — the p.d. is the same.