The current flowing through a wire varies with time according to i = i₀ + t , where i₀ = 10 A and = 4 A s ⁻¹ . Determine the charge that crosses a section of the wire in 10 seconds.

Step-by-step solution

The current flowing through the wire is given by i = dq dt = i₀ + t The charge q crossing a section of the wire in time t is obtained by integrating the current: q = ₀^ t i , dt Substituting the given values i₀ = 10 A and = 4 A s ⁻¹ : q = ₀¹⁰ (10 + 4t) , dt q = [ 10t + 4t^2 2 ]₀¹⁰ q = [ 10t + 2t^2 ]₀¹⁰ q = 10(10) + 2(10)^2 q = 100 + 200 = 300 C