Overview
The lecture covers how to solve a circuit problem involving parallel resistors, current, voltage, and the calculation of electromotive force (emf) in a mixed resistor circuit.
Determining Voltage v1
- v1 is the voltage across a parallel combination, measured by a voltmeter.
- Voltage across all branches in parallel is the same.
- For the branch with 0.6 A current and a 4 Ω resistor, use V = I × R: 0.6 × 4 = 2.4 V.
- Thus, v1 = 2.4 V, which is the voltage across both parallel branches.
Determining Current a1
- a1 is the total current in the main part of the circuit before splitting.
- The current splits at the parallel section: one branch has 0.6 A.
- To find the current in the other branch (with 6 Ω), use I = V/R: 2.4/6 = 0.4 A.
- Total current a1 = 0.6 A + 0.4 A = 1 A.
Calculating the EMF of the Battery
- Use the formula: emf = I × (R + r), where r = internal resistance.
- Current in the main circuit is 1 A; internal resistance r = 0.8 Ω.
- Total external resistance R is the sum of the equivalent parallel and series resistors.
- Calculate parallel resistance: 1/Rp = 1/6 + 1/4 ⇒ Rp = 2.4 Ω.
- Add series resistor: R = 2.4 Ω + 5.8 Ω = 8.2 Ω.
- Plug into the emf formula: emf = 1 × (8.2 + 0.8) = 9 V.
Key Terms & Definitions
- Voltage (V) — Electrical potential difference between two points, measured in volts (V).
- Current (I) — Flow of electric charge, measured in amperes (A).
- Resistance (R) — Opposition to current flow, measured in ohms (Ω).
- Parallel Circuit — Circuit configuration where components share the same voltage.
- Series Circuit — Circuit configuration where current flows through components sequentially.
- EMF (Electromotive Force) — The total energy supplied per coulomb of charge by the source, measured in volts (V).
- Internal Resistance (r) — Resistance within the battery itself.
Action Items / Next Steps
- Practice calculating total resistance for both series and parallel circuits.
- Try more problems involving emf and internal resistance.