DC Circuit with Internal Resistance
A real cell is not an ideal EMF. Inside the dashed box, E drives charge while internal resistance r drops voltage. Terminal voltage is V = E − Ir, and green particles show the current I = E / (R + r).
Parameters
12.0 V
1.0 Ω
10.0 Ω
HKDSE Formula Focus
$I = \dfrac{E}{R+r}$
$V = E - Ir = IR$
$P = I^{2}R \quad \eta = \dfrac{R}{R+r}$
Terminal voltage falls as current rises. Efficiency is the fraction of EMF that appears across the load.
Live Readings
Current I
1.09 A
Terminal V
10.91 V
Internal drop Ir
1.09 V
Load power P
11.90 W
Lost in r
1.19 W
Efficiency η
90.9%
EMF split: useful V vs lost Ir
V on load
Ir inside cell
Typical classroom cell: most of the EMF appears across the load.
Key Concepts
- EMF E is the energy per coulomb supplied by the cell.
- Internal r is inside the cell; it always wastes I²r heat.
- Terminal voltage V = E − Ir equals the load voltage IR.
- Maximum load power when R = r (then η = 50%).