D.C. circuits: components, networks and transients
Key idea: Read topology before calculating, distinguish component and source behaviour, and use shared-current, shared-p.d., shared-charge and exponential models only in the arrangements where they apply.
Before you start: Current Electricity objective chainElectric Fields objective chain
By the end, you can
- Use standard circuit symbols and interpret electrical topology with correct meter placement.
- Apply resistance and resistivity while explaining component I–V and temperature behaviour microscopically.
- Analyse terminal p.d. and power when a source has internal resistance.
- Solve resistor networks and sensor potential dividers.
- Combine capacitors using shared-charge and shared-potential-difference reasoning.
- Represent capacitor charging and discharging with the correct exponential and time constant.
Starting-point self-check
1. Check your starting point
Attempt all six groups without notes and mark the first diagram, material, source, network, capacitance or transient decision you cannot justify. Use the recorded topic diagnostic above when you want scoring and a personalised repair plan.
Internal resistance, terminal p.d. and output power 16(g)
Question 1
A cell has e.m.f. 1.50 V and internal resistance 0.30 Ω supplying a 2.7 Ω load. Find I, terminal p.d. and load power.
Check the model response
I = E/(R + r) = 1.50/3.00 = 0.50 A. Vterminal = E − Ir = 1.35 V, also IR. Pload = I²R = 0.675 W.
repair
2. Repair the common breaks
Use only the correction matching an error, then retry the corresponding diagnostic.
Internal resistance, terminal p.d. and output power 16(g)
Check this idea
Misconception: Terminal p.d. always equals e.m.f.
Repair: When current is supplied, Vterminal = E − Ir; Ir is the internal lost volts.
worked example
3. Follow six worked models
Follow how each solution fixes nodes, axes, source boundary, network reduction, shared capacitor quantity or initial condition before calculating.
Internal resistance, terminal p.d. and output power 16(g)
Model 1
For a source of e.m.f. E and internal resistance r supplying load R, derive terminal p.d. and load power.
Check the model response
Kirchhoff's loop relation gives E = I(R + r), so I = E/(R + r). Terminal p.d. is V = IR = E − Ir. Load power is P = I²R = E²R/(R + r)²; internal heating is I²r.
guided practice
4. Guided practice
Use each hint only to select the correct topology, material model, combination rule or exponential.
Internal resistance, terminal p.d. and output power 16(g)
Question 1
A 2.0 V source with r = 0.50 Ω supplies 1.0 A. Find terminal p.d. and internal power.
Hint: Lost volts are Ir, not r/I.
Check the model response
V = E − Ir = 1.5 V. Internal power is I²r = 0.50 W.
independent practice
5. Independent practice
Solve without repair notes and state graph axes, ideal-meter assumptions, source model and RC initial/final conditions.
Internal resistance, terminal p.d. and output power 16(g)
Question 1
Explain how increasing load current affects terminal p.d., useful output power and internal dissipation.
Check the model response
The lost volts Ir grow, so terminal p.d. E − Ir falls. Useful power is IV = I(E − Ir), while internal dissipation I²r grows. Output power is not simply proportional to current because terminal p.d. changes.
Practice exit check
6. Practice assessment
Use this as extra closed-book practice, then complete the separate recorded assessment in your plan.
Internal resistance, terminal p.d. and output power 16(g)
Question 1
A 12 V source with r = 1.0 Ω supplies a 5.0 Ω load. Find I, terminal p.d., useful power and internal power.
Check the model response
I = 12/6 = 2.0 A. V = 10 V. Useful power = 20 W; internal power = I²r = 4.0 W.
Re-test practice
7. Delayed re-test practice
Return after at least three days and solve these fresh contexts without reopening earlier responses. The recorded plan enforces the delay and uses a separate re-test family for selected-response skill-group evidence.
Internal resistance, terminal p.d. and output power 16(g)
Question 1
A 1.8 V cell supplies 0.60 A and has terminal p.d. 1.5 V. Find r.
Check the model response
Lost volts = 1.8 − 1.5 = 0.30 V, so r = 0.30/0.60 = 0.50 Ω.