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Q. 72

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 927

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Illustration

Short Answer

Consider the parallel RLC circuit shown in .

a. Show that the current drawn from the emf is

Hint: Start with a phasor that is common to all three circuit elements.

b. What is in the limits and ?

c. Find the frequency for which is a minimum.

d. Sketch a graph of versus .

(a) The proof of the current drawn from emf is given below.

(b) in the limits and .

(c) The frequency for which is a minimum is

(d) The graph of versus is given below.

See the step by step solution

Step by Step Solution

Part(a) Step 1: Given information

We have been given that the parallel RLC circuit shown in .

We need to show that the current drawn from the emf is

Part(a) Step 2: Simplify

We know the formula:

(Let this equation be )

where, is the total current in RLC circuit, is the current passing through resistor, is the current passing through inductor and is the current passing through capacitor.

Now, , where is emf and is the impedance.

, where is resistance.

, where is inductance.

, where is capacitance.

Now, substitute the values of in equation , we get:

Rearranging the terms, we get:

Now substitute , we get:

Hence Proved.

Part(b) Step 1: Given information

We have been given that the parallel RLC circuit shown in .

We need to find in the limits and .

Part(b) Step 2: Simplify

We know that when , then

If , this means there is no hinderance in the path of current.

So, we can say .

Part(c) Step 1: Given information

We have been given that the parallel RLC circuit shown in .

We need to find the frequency for which is minimum.

Part(c) Step 2: Simplify

The frequency for is minimum when:

, where (from Part(a))

Now substitute , we get:

The frequency for which is minimum is .

Part(d) Step 1: Given information

We have been given that the parallel RLC circuit shown in .

We need to sketch a graph of versus .

Part (d) Step 2: Graph

Graph of versus

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