SPM Physics: AHA! V–I Graph – EMF First, Then r!

 

When analyzing a graph of potential difference (V) against current (I), the key is to think EMF first. The intercept and gradient reveal everything you need:

Equation of a cell:

$$V=E-Ir$$

Compare with linear form:

$$y=c+mx$$

• Intercept (c) = EMF,
  $E$

• Gradient (m) = –r (negative of internal resistance)

Example:

From the graph:

• At
  $I=0$
  ,
  $E=3.0V$
  .

• Gradient:
  $\frac{0.5-3.0}{3.0-0}=-0.83$
  .

• Therefore,
  $r=0.83\mathrm{\Omega }$
  .

Exam traps:

• Forgetting that the intercept gives EMF.

• Misinterpreting the gradient sign.

• Jumping straight to calculation without identifying the linear form.

👉 Success flow: Equation → Linear form → Intercept = EMF → Gradient = –r → Internal resistance.

AHA! EMF first, resistance next. Not by sight, but by INSIGHT!

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