Given Information:
Voltage = 6.16 V
Resistance = 500 Ω
Capacitance = 1.5 µF
Required Information:
Initial current = I = ?
Time constant = τ = ?
Current after 1 time constant = ?
Voltage after 1 time constant = ?
Answer:
I₀ = 0.0123 A
τ = 0.00075 sec
I = 0.00452 A
V = 3.89 V
Explanation:
(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.
A )The initial current in the circuit ( I₁ ) = 0.0123 A
B) The RC time constant is = 7.5 * 10⁻⁴ sec
C) The current after one time constant = 0.00452 A
D) The voltage on the capacitor after the one time constant = 3.89 V
Given data :
Resistance ( R ) = 500 -Ω
Capacitance of the capacitor ( C ) = 1.50-μF
Voltage source = 6.16-V
A) Calculate the Initial current found in the circuit
I₁ = voltage / resistance of resistor
= 6.16 / 500 = 0.0123 A
B) Calculate for the value of RC time constant ( i.e. time to fully charge capacitor)
RC time constant ( i ) = R * C
= 500 * 1.50 * 10⁻⁶ = 7.5 * 10⁻⁴ sec.
C) Determine current after one time constant
I = [tex]I_{1} e^{(-τ/RC)}[/tex] --- ( 1 ) given that i = Rc
I = 0.0123 * e^(-1)
∴ I ( current after one time constant ) = 0.00452 A
D) Voltage on capacitor after one time constant
V = V₀(1 - e^(-τ/RC))
= 6.16 ( 1 - e^(-1) )
= 6.16 ( 1 - 0.3679 )
= 3.89 V
Hence we can conclude that The initial current in the circuit ( I₁ ) = 0.0123 A The RC time constant is = 7.5 * 10⁻⁴ sec , The current after one time constant = 0.00452 A and The voltage on the capacitor after the one time constant = 3.89 V .
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