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Q. 68

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
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Illustration

Short Answer

shows voltage and current graphs for a series RLC circuit.

a. What is the resistance ?

b. If , what is the resonance frequency in ?

(a) The resistance is .

(b) If , the resonance frequency is .

See the step by step solution

Step by Step Solution

Part(a) Step 1: Given information

We have been given that the voltage and current graphs for a series RLC circuit in .

We need to find the resistance .

Part(a) Step 2: Simplify

In RLC circuit, the total resistance represents the impedance in the circuit.

We can calculate the root mean square voltage by using impedance because the circuit draws root mean square current ().

We know the formula that the emf () is given by:

(Let this equation be ())

where is the inductive reactance and is the capacitive reactance for RLC circuit.

The phase angle () between the current and the emf is given by the formula :

(Let this equation be ())

Substituting the equation in equation , we get:

Rearranging the terms, we get:

(Let this equation be ())

Now substitute the values of in equation () from the graph given in to find the value of ,

Part(b) Step 1: Given information

We have been given that the voltage and current graphs for a series RLC circuit in .

We need to find the resonance frequency when .

Part(b) Step 2: Simplify

The time period in the given graph is .

The end frequency is .

We know that the resonance frequency occurs when , where is the capacitive reactance and is the inductive reactance.

Now, find the Capacitance by equating :

, where is inductance and is capacitance.

Rearranging the terms, we get:

The resonant angular frequency is given by :

(Let this equation be ())

Now use the equation () obtained in Part(a) to get the resonance frequency () :

(Using equation )

Substituting and , we get:

Rearranging the terms, we get:

Substituting the values of , we get:

The resonance frequency is when .

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