Question

For a parallel RLC driven by a current source ῖ, find values for R, L and C if:

a). |ῖ| = 2eʲ⁰°μA, |ṽ| max =125 mV, Q₀ = 40, and F₀ = 1 MHz, where |ṽ| max represents the maximum magnitude of the voltage across the parallel elements

Answer 1

To find R, L, and C for a parallel RLC circuit with given |ῖ|, |ṽ| max, Q₀, and F₀, we use formulas for resonance and quality factor. The actual values require algebraic calculations using the provided formulas for Vmax, Q, and F₀, based on the given properties of the circuit.

Step-by-step explanation:

To solve for the values of R, L, and C in a parallel RLC circuit driven by a current source with a magnitude of 2μA, given that the maximum voltage magnitude |ṽ| max is 125 mV, the quality factor Q₀ is 40, and the resonance frequency F₀ is 1 MHz, we can use the following formulas:

• The peak voltage across the RLC combination Vmax = I * Z, where Z is the impedance at resonance.
• The quality factor Q = R / Z, where Z is the total impedance at resonance.
• The total impedance Z = R / Q₀, by rearranging the formula for Q.
• The resonant frequency F₀ = 1 / (2π√(LC)).

We are given that F₀ is 1 MHz, so we can calculate L and C using the resonant frequency formula. After finding L and C, we can use the Q factor and the given Vmax to solve for the impedance Z, and then calculate R using Q and Z. To calculate the actual values, one would typically use algebraic manipulation and substitute the given quantities into these equations. For the specifics of this calculation, additional context is necessary as the relationships for a parallel RLC circuit differ from those of a series circuit and depend on whether the elements are in resonance.