A capacitor with a capacitance of 8.0 F is wired to a battery of emf 6.0 V via a resistance of 24 . Determine the current in the circuit exactly one time constant after the connections are made.

Step-by-step solution

The current in an RC circuit during charging is given by the equation: I(t) = I₀ e^ -t/ where I₀ = V R is the initial current and = RC is the time constant. At exactly one time constant, t = , the current becomes: I( ) = I₀ e⁻¹ = I₀ e The initial current I₀ is: I₀ = 6.0 24 = 0.25 A Substituting I₀ and the value of e 2.718 into the equation for current: I( ) = 0.25 2.718 0.09 A