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AQA GCSE · Question 03.2 · Electricity

Which graph shows the relationship between the resistance of a wire at constant temperature and its length?

Answer options:

A.

<svg width='150' height='120' xmlns='http://www.w3.org/2000/svg'><line x1='20' y1='100' x2='130' y2='100' stroke='black' marker-end='url(#arrowH)'/><line x1='20' y1='100' x2='20' y2='10' stroke='black' marker-end='url(#arrowV)'/><text x='75' y='115' text-anchor='middle'>Length</text><text x='10' y='60' text-anchor='middle' transform='rotate(-90,10,60)'>Resistance</text><line x1='30' y1='20' x2='120' y2='90' stroke='black' stroke-width='2'/><defs><marker id='arrowH' viewBox='0 0 10 10' refX='8' refY='5' markerWidth='6' markerHeight='6' orient='auto'><path d='M 0 0 L 10 5 L 0 10 z' fill='black'/></marker><marker id='arrowV' viewBox='0 0 10 10' refX='5' refY='2' markerWidth='6' markerHeight='6' orient='auto'><path d='M 0 10 L 5 0 L 10 10 z' fill='black'/></marker></defs></svg>

B.

<svg width='150' height='120' xmlns='http://www.w3.org/2000/svg'><line x1='20' y1='100' x2='130' y2='100' stroke='black' marker-end='url(#arrowH)'/><line x1='20' y1='100' x2='20' y2='10' stroke='black' marker-end='url(#arrowV)'/><text x='75' y='115' text-anchor='middle'>Length</text><text x='10' y='60' text-anchor='middle' transform='rotate(-90,10,60)'>Resistance</text><path d='M 30 95 C 50 90, 70 40, 120 35' stroke='black' stroke-width='2' fill='none'/><defs><marker id='arrowH' viewBox='0 0 10 10' refX='8' refY='5' markerWidth='6' markerHeight='6' orient='auto'><path d='M 0 0 L 10 5 L 0 10 z' fill='black'/></marker><marker id='arrowV' viewBox='0 0 10 10' refX='5' refY='2' markerWidth='6' markerHeight='6' orient='auto'><path d='M 0 10 L 5 0 L 10 10 z' fill='black'/></marker></defs></svg>

C.

<svg width='150' height='120' xmlns='http://www.w3.org/2000/svg'><line x1='20' y1='100' x2='130' y2='100' stroke='black' marker-end='url(#arrowH)'/><line x1='20' y1='100' x2='20' y2='10' stroke='black' marker-end='url(#arrowV)'/><text x='75' y='115' text-anchor='middle'>Length</text><text x='10' y='60' text-anchor='middle' transform='rotate(-90,10,60)'>Resistance</text><line x1='20' y1='100' x2='120' y2='20' stroke='black' stroke-width='2'/><defs><marker id='arrowH' viewBox='0 0 10 10' refX='8' refY='5' markerWidth='6' markerHeight='6' orient='auto'><path d='M 0 0 L 10 5 L 0 10 z' fill='black'/></marker><marker id='arrowV' viewBox='0 0 10 10' refX='5' refY='2' markerWidth='6' markerHeight='6' orient='auto'><path d='M 0 10 L 5 0 L 10 10 z' fill='black'/></marker></defs></svg>

How to approach this question

Recall the relationship between the resistance of a wire and its length. Are they directly proportional, inversely proportional, or something else? A directly proportional relationship is represented by a straight line graph that passes through the origin.

Full Answer

C.<svg width='150' height='120' xmlns='http://www.w3.org/2000/svg'><line x1='20' y1='100' x2='130' y2='100' stroke='black' marker-end='url(#arrowH)'/><line x1='20' y1='100' x2='20' y2='10' stroke='black' marker-end='url(#arrowV)'/><text x='75' y='115' text-anchor='middle'>Length</text><text x='10' y='60' text-anchor='middle' transform='rotate(-90,10,60)'>Resistance</text><line x1='20' y1='100' x2='120' y2='20' stroke='black' stroke-width='2'/><defs><marker id='arrowH' viewBox='0 0 10 10' refX='8' refY='5' markerWidth='6' markerHeight='6' orient='auto'><path d='M 0 0 L 10 5 L 0 10 z' fill='black'/></marker><marker id='arrowV' viewBox='0 0 10 10' refX='5' refY='2' markerWidth='6' markerHeight='6' orient='auto'><path d='M 0 10 L 5 0 L 10 10 z' fill='black'/></marker></defs></svg>✓ Correct
The third graph, showing a straight line through the origin with a positive gradient.
The resistance of a wire is directly proportional to its length, assuming other factors like temperature and cross-sectional area are constant. This means that if you double the length of the wire, you double its resistance. A relationship of direct proportionality is represented graphically by a straight line passing through the origin (0,0). The third graph is the only one that shows this relationship.

Common mistakes

✗ Choosing the first graph, which shows an inverse relationship. ✗ Choosing the second graph, which shows a non-linear relationship.
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