Reduce the external network
Two identical resistors R in parallel have equivalent resistance R/2. That equivalent load is in series with the battery’s internal resistance.
SKILLS · CHEMISTRY & PHYSICS
Circuits & branch power
A new parallel branch increases total current, but a real battery can deliver less voltage to each branch. Follow the whole circuit before calculating one component’s power.
01 · THE IDEA
The internal resistor carries total current; each external branch receives terminal voltage.
I = ε / (r + Rload); Vterminal = ε − Ir; Pbranch = Vterminal² / Rbranch
Model the discharging battery as an ideal emf ε in series with a fixed internal resistance r. External resistors are fixed, wires are ideal, and the circuit is at steady state.
Separate total and branch current
Total current passes through r before splitting. Branch current is terminal voltage divided by that branch’s resistance; it is not automatically the battery current.
Use the right power expression
At a fixed branch resistance, power scales as voltage squared. For an ideal source with r = 0, adding a parallel branch leaves the original branch’s voltage and power unchanged.
CHANGE ONE PART OF THE MODEL
One source, one or two branches
The emf is 18 V. Each external branch has a 6 Ω resistor. Compare a source with 3 Ω internal resistance with an ideal source.
Total current2 A
Terminal voltage12 V
Power in X24 W
I = 18 / (3 + 6) = 2 A; current in X = 2 A
Adding a parallel branch raises total current and the internal voltage drop, reducing power in X.
02 · WORKED EXAMPLES
Follow the setup, then the numbers
1. Adding a branch to a real battery
An 18 V battery has internal resistance 3 Ω and powers one 6 Ω resistor X. Add another 6 Ω resistor in parallel with X.
- Single branch: I = 18/(3 + 6) = 2 A; terminal voltage = 12 V.
- Two branches: external load = 3 Ω; total I = 18/(3 + 3) = 3 A.
- The internal drop is now 3 × 3 = 9 V, leaving 9 V across each branch.
- X current falls from 12/6 = 2 A to 9/6 = 1.5 A, although total current rises.
Carry this forward: The battery current and the current in X can move in opposite directions.
2. Convert a voltage ratio into a power ratio
For the same circuit, compare power in X before and after adding the branch.
- Before: PX = 12²/6 = 24 W. After: PX = 9²/6 = 13.5 W.
- Power ratio = 13.5/24 = 0.5625.
- Equivalently, with X fixed: (9/12)² = 0.5625.
Carry this forward: A voltage fraction of 0.75 gives a power fraction of 0.5625, not 0.75.
03 · TRY IT IN DIFFERENT FORMS
Practice in different forms
For each question, identify the requested quantity and write the setup before calculating. Use a hint if needed, then choose an answer to see the explanation.
Untimed learning practice. These responses stay on this page and reset when you leave or reload; they do not change your test results.
QUESTION 1 / 4 · C/P
Find the terminal voltage
A battery has emf 24 V and internal resistance 4 Ω. It powers two identical 8 Ω resistors in parallel. What is the voltage across either external resistor?
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TAKE INTO A FRESH PASSAGE
Your setup checklist
- Reduce the external resistor network.
- Add internal resistance before finding battery current.
- Calculate terminal voltage before branch current or power.
- For a fixed resistor, square voltage or current ratios when comparing power.
Before calculating, explain what each term represents and what the requested answer would mean.
Concept references
All scenarios and questions here are original learning exercises. These references support the underlying concepts; the simplified assumptions are stated within each example.