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.
Capacitors in series and parallel 16(k)
Question 1
Find the equivalent capacitance of 6.0 μF and 3.0 μF first in series and then in parallel.
Check the model response
Series: 1/C = 1/6 + 1/3 in μF⁻¹, so C = 2.0 μF. Parallel: C = 6.0 + 3.0 = 9.0 μF.
repair
2. Repair the common breaks
Use only the correction matching an error, then retry the corresponding diagnostic.
Capacitors in series and parallel 16(k)
Check this idea
Misconception: Capacitances combine exactly like resistances.
Repair: Capacitances add in parallel; reciprocal capacitances add in series.
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.
Capacitors in series and parallel 16(k)
Model 1
Explain why capacitor-combination rules are opposite in form to resistor rules.
Check the model response
Parallel capacitors share p.d. and their plate charges add, so Ceq = ΣC. Series capacitors carry equal charge while their p.d.s add, so 1/Ceq = Σ(1/C). The result follows from Q = CV, not from memorising an analogy.
guided practice
4. Guided practice
Use each hint only to select the correct topology, material model, combination rule or exponential.
Capacitors in series and parallel 16(k)
Question 1
Three 12 μF capacitors are in series. Find Ceq.
Hint: Add reciprocals, not capacitances.
Check the model response
For equal capacitors in series, Ceq = C/3 = 4.0 μF.
independent practice
5. Independent practice
Solve without repair notes and state graph axes, ideal-meter assumptions, source model and RC initial/final conditions.
Capacitors in series and parallel 16(k)
Question 1
Derive both capacitor rules from shared charge or shared p.d.
Check the model response
Parallel capacitors share V, so Qtotal = ΣCiV = CeqV and Ceq = ΣCi. Series capacitors have equal Q and Vtotal = Σ(Q/Ci) = Q/Ceq, giving 1/Ceq = Σ(1/Ci).
Practice exit check
6. Practice assessment
Use this as extra closed-book practice, then complete the separate recorded assessment in your plan.
Capacitors in series and parallel 16(k)
Question 1
Find Ceq for 4.0 μF in parallel with a series pair of 6.0 μF and 3.0 μF.
Check the model response
The series pair is 2.0 μF. In parallel with 4.0 μF, total capacitance is 6.0 μF.
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.
Capacitors in series and parallel 16(k)
Question 1
Two equal capacitors C are connected first in series and then in parallel. State both equivalent capacitances.
Check the model response
Series gives C/2; parallel gives 2C.