In the figure , the total resistance is 13.0 k \Omega, and the battery's emf is 32.0 V. If the time constant is measured to be 40.0 \mu s. Calculate the total capacitance of the circuit.
Without the circuit, it is hard to tell.
It could be as simple as the RC time constant
RC=40E-6 seconds, you know R, calculate C
There is no figure. Have you noticed that?
In an RC circuit, the time constant is RC.
Solve for C
To calculate the total capacitance of the circuit, we can use the formula for the time constant (τ) of an RC circuit:
τ = RC
where:
- τ is the time constant in seconds
- R is the total resistance in ohms
- C is the total capacitance in farads
In this case, we are given:
- total resistance (R) = 13.0 kΩ = 13.0 × 10^3 Ω
- time constant (τ) = 40.0 μs = 40.0 × 10^-6 s
We need to rearrange the formula to solve for capacitance (C):
C = τ / R
1. Convert the resistance to ohms:
R = 13.0 kΩ = 13.0 × 10^3 Ω
2. Convert the time constant to seconds:
τ = 40.0 μs = 40.0 × 10^-6 s
3. Substitute the values into the formula:
C = (40.0 × 10^-6 s) / (13.0 × 10^3 Ω)
4. Simplify the expression:
C = 3.08 × 10^-9 F
5. Final answer:
The total capacitance of the circuit is 3.08 nanofarads (nF).