B.5 · IB Physics
DC circuits and internal resistance
A real cell has internal resistance. Connect one load or two, watch the terminal p.d. fall as the current rises, and find the load that draws the most power.
Predict first
Start from the default settings (ε = 6.0 V, r = 0.5 Ω, single load R₁ = 4.0 Ω). If you raise R₁ to 8.0 Ω, what happens to the terminal p.d. V?
A larger load takes less current, I = ε/(R + r) falls from 1.33 A to 0.706 A, so less p.d. is lost across the internal resistance. V = ε − Ir therefore rises towards ε.
Check it in the model: Move the Load R₁ slider from 4.0 to 8.0 Ω and compare the Terminal p.d. V readout.
conventional current (dots) load resistors graph operating point
Presets
terminal p.d. V = ε − I r
P = I² R ; η = R ÷ (R + r)
series: R = R₁ + R₂
parallel: 1/R = 1/R₁ + 1/R₂
Try this
- With one load, move R₁ from 0.1 Ω to 20 Ω and watch the operating point slide along the V–I line. Where is the terminal p.d. closest to the EMF?
- Use the Matched load preset (r = 2.0 Ω, R₁ = 2.0 Ω). Check the load power is the maximum on the P–R graph, then read the efficiency.
- Choose “R₁ and R₂ in parallel” with both at 4.0 Ω and compare the current and power with a single 4.0 Ω load. Then try series.
Exam tip: the terminal p.d. is V = ε − Ir, so a graph of V against I is a straight line with gradient −r and intercept ε; maximum power transfer happens when R = r, but the efficiency is only 50 % there.