Answer:
initial current I₀ = 0.0123 A
RC time constant τ = 0.00075 sec
current after one time constant I = 0.00452 A
voltage on the capacitor after one time constant V = 3.89 V
Explanation:
Given that,
Voltage = 6.16 V
Resistance = 500 Ω
Capacitance = 1.5 µF
(a) What is the initial current?
The initial current can be found using
I₀ = Voltage/Resistance
I₀ = 6.16/500
I₀ = 0.0123 A
(b) What is the RC time constant?
The time constant τ provides the information about how long it will take to charge the capacitor.
τ = R*C
τ = 500*1.5x10⁻⁶
τ = 0.00075 sec
(c) What is the current after one time constant?
I = I₀e^(-τ/RC)
I = 0.0123*e^(-1) (0.00075/0.00075 = 1)
I = 0.00452 A
(d) What is the voltage on the capacitor after one time constant?
V = V₀(1 - e^(-τ/RC))
Where V₀ is the initial voltage 6.16 V
V = 6.16(1 - e^(-1))
V = 6.16*0.63212
V = 3.89 V
That means the capacitor will charge up to 3.89 V in one time constant
Answer:
Explanation:
Given an RC circuit to analyze
R=500Ω
C=1.50-μF uncharged
Emf(V)=6.16V
Series connection
a. Initial current, since the capacitor is initially uncharged then, the voltage appears at the resistor
Using ohms law
V=iR
Then, i=V/R
i=6.16/500
i=0.01232 Amps
i=12.32 mA.
b. The time constant is given as
τ=RC
τ=500×1.5×10^-6
τ=0.00075second
τ=0.75 ms
c. What is current after 1 time constant
Current in a series RC circuit is given as
Time after I time constant is
t=1 ×τ
t= τ
i=V/R exp(-t/RC)
Where RC= τ
i=V/Rexp(-t/ τ)
i=6.16/500exp(-1), since t= τ
i=0.004532A
I=4.532mA
d. Voltage after one time constant
Voltage of a series RC circuit(charging) is given as
Again, t= τ
V=Vo(1 - exp(-t/ τ)),
V=6.16(1-exp(-1))
V=6.16(1-0.3679)
V=6.16×0.632
V=3.89Volts
V=3.89V
V=
