Question Detail

The voltage across the capacitor in a charging RC circuit is given by Vc(t) = Vbattery(1 - e-t/τ), where τ is the time constant. The voltage across the resistor is Vr(t) = Vbattery - Vc(t) = Vbatterye-t/τ.Given:Capacitance C = 10 µF = 10 × 10-6 F = 10-5 FResistance R = 400 kΩ = 400 × 103 Ω = 4 × 105 ΩBattery voltage Vbattery = 24 VTime t = 1 sFirst, calculate the time constant τ = RC:τ = (4 × 105 Ω) × (10-5 F) = 4 sNow, calculate the voltage across the resistor after 1s:Vr(t) = 24 V × e-1/4Vr(t) = 24 V × e-0.25Vr(t) = 24 V × 0.7788Vr(t) ≈ 18.69 VRounding to one decimal place, the voltage across the resistor is 18.7V.