Lesson summary
10.2.3 Resistors in Series — AS PHYSICS 9702 notes: Derive and use R = R₁ + R₂ + … for resistors in series.Current — it is the same through all the resistors.Potential difference — it is shared between all the resistors.Combined resistance — it is the sum of the individual resist…
- What the symbols mean
- Separate p.d.s
- Rearranging
- Effect of adding resistors
- Components
- Reciprocal
Section 1 of 6Series circuit rules
Current
- Current it is the same through all the resistors.
Potential difference
- Potential difference it is shared between all the resistors.
Combined resistance
- Combined resistance it is the sum of the individual resistances.
Section 2 of 6Derivation from Kirchhoff’s laws
1
The same current I flows through each resistor.
2
By Kirchhoff’s second law, the supply p.d. equals the sum of the p.d.s: V = V1 + V2.
3
Using V = IR for each, IR = IR1 + IR2.
4
Dividing by I gives R = R1 + R2.
Section 3 of 6The equation
1Equation
- R = R1 + R2 + …What the symbols mean: RT = total resistance of resistors in series (Ω) · R1, R2 = the separate resistances (Ω)
2Separate p.d.s
- Separate p.d.s each resistor connected in series has its own separate potential difference.
3Rearranging
- Rearranging an unknown resistor is found from R2 = R − (R1 + R3).
4Effect of adding resistors
- Effect of adding resistors the combined resistance increases.
Section 4 of 6More from the specification
More from the specification
Series resistor voltage and power
- Series resistor voltage and power potential differences divide proportionally across series resistances, dissipating electrical power according to current squared times resistance.
Resistors in series and energy conservation
- In a closed series circuit, the same current flows through all components,
- and the total potential difference across the circuit equals the sum of individual p.d.s,
- giving combined resistance R = R1 + R2 + R3.
Resistors in parallel rule
- For parallel circuit branches connected across common junctions, the reciprocal of the total equivalent resistance equals the sum of the reciprocals of individual resistances: 1/Rp = 1/R1 + 1/R2 + 1/R3.
Kirchhoff's laws in problem solving
- Kirchhoff's first law applies conservation of charge at any junction,
- (sum of Iin = sum of Iout)
- while Kirchhoff's second law applies conservation of energy around any closed loop.
- (sum of EMF = sum of IR)
Potential divider circuits
- When solving problems with series resistors, the potential difference across any individual resistor is proportional to its fraction of the total series resistance (Vout = Vin * (R2 / (R1 + R2))).
Resistors in series and energy conservation
- In a closed series circuit, the same current flows through all components,
- and the total potential difference across the circuit equals the sum of individual p.d.s,
- giving combined resistance R = R1 + R2 + R3.
Resistors in parallel rule
- For parallel circuit branches connected across common junctions, the reciprocal of the total equivalent resistance equals the sum of the reciprocals of individual resistances: 1/Rp = 1/R1 + 1/R2 + 1/R3.
Kirchhoff's laws in problem solving
- Kirchhoff's first law applies conservation of charge at any junction,
- (sum of Iin = sum of Iout)
- while Kirchhoff's second law applies conservation of energy around any closed loop.
- (sum of EMF = sum of IR)
Potential divider circuits
- When solving problems with series resistors, the potential difference across any individual resistor is proportional to its fraction of the total series resistance (Vout = Vin * (R2 / (R1 + R2))).
Ammeter
- Component that measures current.
Voltmeter
- Instrument that measures p.d., connected in parallel.
Charge
- Quantity of electricity in coulombs, Q = It.What the symbols mean: Q = charge (C) · I = current (A) · t = time (s)
Series circuit
- Circuit with components connected one after another in a single loop.
Parallel circuit
- Circuit with branches; same p.d. across each branch.
Closed circuit
- Complete loop with a source in which current can flow
Energy 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)
Parallel
- Components on separate branches, each with the full e.m.f.
Junction
- Place where a pipe splits or joins; flow rates add.
Components
- Perpendicular parts of a vector that add to give the vector.
Reciprocal
- The value 1/x; the calculator button is x−1.
Section 5 of 6Key terms
| Term | Meaning |
|---|---|
| Series circuit | Components connected end to end so the same current passes through each. |
| Combined resistance | Single resistance that could replace the network and draw the same current. |
| Kirchhoff’s second law | Total e.m.f. equals the sum of the p.d.s across the components. |
| Potential difference | Energy transferred per unit charge between two points. |
Section 6 of 6Exam technique
1
Adding the reciprocals for resistors in series — only add the resistances.
2
Thinking the current is shared in series — the current is the same.
3
Forgetting that the combined resistance is larger than any single resistor.
4
Using the wrong resistor values when rearranging.