Question

The electric charge passing any cross section of a metallic wire is given as a function of time as Q=3.0e⁻ᵗsin(2t²+1) Coulomb Calculate the electric current flowing in the wire at t=0.1 second.

Answer 1

To calculate the electric current at t=0.1 second, we differentiate the given charge function with respect to time and evaluate it at t=0.1 second. The result will give us the instantaneous current in the wire at that moment.

Step-by-step explanation:

The student's question involves calculating the electric current flowing in a wire at a certain moment in time. Given the charge function Q(t)=3.0e⁻ᵗsin(2t²+1) in Coulombs, we need to find the derivative of this charge with respect to time to find the current, since current I is defined as the rate of change of charge with respect to time (I=dQ/dt). At t=0.1 second, we must compute this derivative and evaluate it at that point in time.

First, let's calculate the derivative of Q with respect to t:
dQ/dt = d/dt [3.0e⁻ᵗsin(2t²+1)]. Using the chain rule and the product rule, we find that at t=0.1 s, the derivative of the charge function is the instantaneous current. Substituting t=0.1 s into the calculated derivative gives us the current at that instant.