What if the frequency is now increased to f = 69 Hz, and we want to keep the impedance unchanged? (A) What new resistance should we use to achieve this goal? R = Ω (B) What is the phase angle (in degrees) between the current and the voltage now? ϕ = ° (C) Find the maximum voltages across each element.

Complete Question

A series RLC circuit has R = 405 Ω, L = 1.40 H, C = 3 µF. It is connected to an AC source with f = 60.0 Hz and ΔVmax = 150 V. What if the frequency is now increased to f =  69 Hz, and we want to keep the impedance unchanged? (A) What new resistance should we use to achieve this goal? R = Ω (B) What is the phase angle (in degrees) between the current and the voltage now? ϕ = ° (C) Find the maximum voltages across each element.

A

B

C

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Explanation:

From the question we are told that

   The resistance is  

    The inductance is  L = 1.40 H

    The capacitance is  

    The original  frequency is

    The new frequency is  

Generally the reactance of the inductor is mathematically represented as

=>

=>

Generally the reactance of the capacitor is mathematically represented as

=>

Generally the impedance of the circuit is mathematically  represented as

=>    

=>    

Generally when the frequency is changed , the reactance of the inductor becomes

 =>  

Generally when the frequency is changed , the reactance of the capacitor becomes

=>

Generally the new resistance is mathematically represented as

=>  

=>  

=>  

Generally the phase angle is mathematically represented as

=>    

=>  

Generally the maximum current flowing through the circuit is mathematically represented as

=>    

=>    

Generally  the maximum voltage across the capacitor is

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Generally  the maximum voltage across the inductor is

=>  

Generally  the maximum voltage across the resistor is

=>  

like poles repel so keep pushing north to north and repels funny to see this