The current in a conductor is expressed as I=3 t²+4 t³, where I is in Ampere and t is in second. The amount of electric charge that flows through a section of the conductor during t=1 s to t=2 s is __________ C.

Solution

Physics sir · 3 steps

Current is the rate of flow of charge, so integrate I over time from 1 s to 2 s to get the charge.

1. Charge from current. Current is I = dQ/dt, so the charge in a small time dt is dQ = I dt. Here the current changes with time, so you cannot just multiply one value of I by the time interval. You have to add up I dt with an integral.

   Q = ∫₁² (3t² + 4t³) dt = [ t³ + t⁴ ]₁²

2. Put in limits. At t = 2 s: 2³ + 2⁴ = 8 + 16 = 24. At t = 1 s: 1³ + 1⁴ = 1 + 1 = 2.
3. So. Q = 24 - 2 = 22 C.

The common slip: 24. Putting in only the upper limit t = 2 s gives 24, not 22. The value t³ + t⁴ = 2 at t = 1 s must be subtracted.

The idea to keep. Whenever current varies with time, charge is the area under the I–t graph: Q = ∫ I dt between the given instants. Always subtract the value at the lower limit.

Answer from the NTA final answer key. Solution by PrepWiser.