if a circuit has a3.9k resistor and a5uf capacitor, find the current flow in the circuit at 0.005 seconds, if the maximum current flow in the circuit is 105mA
T = RC = 3.9K * 5uF = 19.5 Milliseconds
= Time Constant.
t/T = 5ms / 19.5ms = 0.256.
i = 105*e^-(t/T),
i = 105*e^(-0.256) = 81.3mA.
NOTE: If R was in ohms and C in Farads,
the Time Constant would be in seconds.
To find the current flow in the circuit at a specific time, we need to use the concept of charging and discharging of a capacitor in an RC circuit. The current flow in the circuit can be calculated using Ohm's law and the equation for charging a capacitor.
Step 1: Calculate the time constant (τ)
The time constant (τ) is the product of the resistance (R) and the capacitance (C) in an RC circuit. It represents the time it takes for the capacitor to charge or discharge to approximately 63.2% of its maximum voltage.
τ = R * C
Given: R = 3.9kΩ (kilo-ohms) = 3900Ω, C = 5μF (microfarads) = 5 * 10^(-6) F (farads)
τ = 3900Ω * 5 * 10^(-6) F
= 19.5ms (milliseconds)
Step 2: Determine the percentage of charge at a specific time
To compute the current flow in the circuit at a specific time, we need to calculate how much charge has been stored in the capacitor at that time in relation to its maximum charge.
t = 0.005s (seconds) (given)
First, we need to find the ratio of the current time to the time constant:
t / τ = 0.005s / 19.5ms
= 0.256
Next, we find the percentage of charge stored in the capacitor:
Percentage of charge = (1 - e^(-t/τ)) * 100%
e = 2.71828 (the base of the natural logarithm)
Percentage of charge = (1 - e^(-0.256)) * 100%
Step 3: Calculate the current flow
Finally, we can calculate the current flow in the circuit using Ohm's law:
I = V / R
Given: Maximum current flow = 105mA (milliamperes) = 105 * 10^(-3) A (amperes)
The maximum current flow occurs when the capacitor is fully charged. At this point, the voltage across the resistor is equal to the maximum voltage across the capacitor.
V = I * R
V = (105 * 10^(-3) A) * 3900Ω
= 409.5V
Now, we can use the percentage of charge to calculate the current flow at the specific time:
I = (Percentage of charge / 100%) * (Maximum current flow)
Plug in the values and calculate the current flow:
I = ((1 - e^(-0.256)) * 100%) * (105 * 10^(-3) A)