A 100 F capacitor is joined to a 24 V battery via a 1.0 M resistor. Which of the following best describes the qualitative graph between current and time for the first 10 minutes?

Step-by-step solution

The given circuit is an RC charging circuit. The time constant of the circuit is given by = RC . Substituting the given values: = (1.0 10^6 ) (100 10⁻⁶ F ) = 100 s The initial current in the circuit at t = 0 is: I₀ = V R = 24 1.0 10^6 = 24 A The current in an RC circuit during charging varies with time according to the equation: I(t) = I₀ e^ -t/ I(t) = 24 e^ -t/100 A This equation represents an exponentially decaying curve. At t = 0 , the current is 24 A , and as time progresses, it exponentially approaches zero. F