Figure below shows a plot of current I through the cross-section of a wire over a time interval of 12s. How much charge flows through the wire during this time period?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 50 C
Current is the rate of flow of charge, \( I = dq/dt \), so the charge is the area under the I-t graph, \( q = \int I\,dt \).
Readings from the graph:
\( 0\ \text{to}\ 4\,\mathrm{s}:\ I\ \text{rises from 0 to}\ 5\,\mathrm{A} \)
\( 4\ \text{to}\ 12\,\mathrm{s}:\ I = 5\,\mathrm{A} \)
Triangle from 0 to 4 s:
\( \displaystyle q_1 = \frac{1}{2} \times 4\,\mathrm{s} \times 5\,\mathrm{A} = 10\,\mathrm{C} \)
Rectangle from 4 s to 12 s:
\( q_2 = (12 - 4)\,\mathrm{s} \times 5\,\mathrm{A} = 40\,\mathrm{C} \)
\( q = q_1 + q_2 = 10\,\mathrm{C} + 40\,\mathrm{C} = 50\,\mathrm{C} \)