in a parallel RLC circuit you have
L=100mH
and
i= inductor current
i=50e^(-4000t)-10e^(-5000t) mA
how do you find R and C??
To find the values of R (resistance) and C (capacitance) in a parallel RLC circuit, you need additional information. The given information only includes the value of the inductance (L) and the expression for inductor current (i). R and C are not explicitly provided.
To determine R and C, you can use the following steps:
Step 1: Derive the expression for voltage across the inductor (VL) and voltage across the capacitor (VC) using the given information.
- Voltage across the inductor (VL) can be obtained by multiplying the inductance (L) with the derivative of the inductor current (di/dt).
VL = L * (di/dt)
- Voltage across the capacitor (VC) can be found by integrating the expression for current (i) with respect to time (t) and multiplying it by the inverse of the capacitance (C).
VC = (1/C) * ∫i dt
Step 2: Identify the relationship between VL, VC, and the resistance (R).
- In a parallel RLC circuit, the total voltage (VT) across the circuit is equal to the sum of the voltages across each component (VL, VC, and VR, where VR is the voltage across the resistor).
VT = VL + VC + VR
- Since VL and VC are known from Step 1, VR can be obtained as:
VR = VT - (VL + VC)
Step 3: Use the expression for VR to determine the value of R.
- VR can be related to the current (i) and resistance (R) using Ohm's Law:
VR = R * i
- Using the obtained values of VR from Step 2 and the current (i) expression given in the question, you can solve for R.
Step 4: Use the expression for VC to calculate the value of C.
- VC can be related to the current (i) and capacitance (C) using the relationship defined in Step 1:
VC = (1/C) * ∫i dt
- Since VC is known from Step 1 and the expression for current (i) is given, you can solve for C by integrating the expression for i over time (t).
By following these steps, you can find the values of R and C for the parallel RLC circuit. Do note that additional information or constraints might be needed to obtain specific numerical values for R and C.