Internal resistance from slope of I-V graph

Steps:

• The graph of current (I) versus potential difference (V) across the variable resistor is a straight line from (V=0, I=E/r) to (V=E, I=0), where E is emf and r is internal resistance.
• The slope of this line is ΔI/ΔV = -1/r.
• Calculate the slope from the graph (e.g., rise over run gives -0.5 A/V).
• Thus, r = -1/slope = -1/(-0.5) = 2 Ω.

Why C is correct:

• The slope of the I-V line is -1/r by Ohm's law for the cell (E = V + I r), confirming r = 2 Ω matches the graph's slope.

Why the others are wrong:

• A: 0.5 Ω would require slope = -2 A/V, steeper than shown.
• B: 1.6 Ω would require slope ≈ -0.625 A/V, not matching the graph.
• D: 23 Ω would require slope ≈ -0.043 A/V, nearly horizontal, unlike the graph.

Final answer: C