A capacitor with a capacitance of 500 F is connected to a battery via a 10 k resistor. Which of the following statements are true regarding the charge stored on the capacitor during the initial 5 s ?

Step-by-step solution

The time constant of the RC circuit is given by = RC . Substituting the given values: = (10 10^3) (500 10⁻⁶) = 5 s The charge on the capacitor as a function of time is q(t) = q₀(1 - e^ -t/ ) , where q₀ is the maximum steady-state charge. The charge stored during the initial 5 s ( t = ) is: q₁ = q(5) - q(0) = q₀(1 - e⁻¹) 0.632 q₀ The maximum possible charge that can be stored in all subsequent time ( t = 5 s to t ) is: q_ remaining = q( ) - q(5) = q₀ - 0.632 q₀ = 0.368 q₀ Since 0.632 q₀ > 0.368 q₀ , the charge store