Calculating time constant, maximun charge, and current in RC circuit

문제)

R = 1.00 MΩ, C = 5.00 μF, ε = 30.0 V

 

(a) Calculate the time constant of the circuit

(b) Calculate the maximum charge of the capacitor after the switch is closed

(c) Calculate the current in the resistor 10.0s after the switch is closed

 

풀이)

R = 1.00 MΩ = 1.00 × 10^6 Ω

C = 5.00 μF = 5.00 × 10^-6 F

ε = 30.0 V

 

(a)

time constant τ = RC

 

τ = RC = 1.00 × 10^6 Ω × 5.00 × 10^-6 F = 5.00 s

 

(b)

the maximum charge Q = C × ε

 

Q = C × ε = 30.0 V × 5.00 × 10^-6 F = 150 μC = 1.50  × 10^-4 C

 

(c)

the current in the resistor I = ε / R × e^(-t / τ) = ε / R × e^(-t / RC)

 

I = ε / R × e^(-t / τ) = 30.0 V / 1.00 × 10^6 Ω × e^(-10.0s / 5.00s) = 4.06 μA = 4.06 × 10^-6 A