Q. 204.0( 4 Votes )

# Find the value of

Answer :

a) 0.57, b)1, c)1.75

Formula used:

Kirchhoff’s loop rule state that the algebraic sum of all the voltages in a loop will be zero. Or,

Solution:

a)

Given resistances are: 1 Ω,1 Ω,0.1Ω

Applying Loop rule, we can write,

Or,

And i_{1} will be,

In the next figure,

Let i be the current that passes through the middle branch and hence i_{2}-i will pass through the upper branch, as shown in figure.

By applying loop rule in AFEDA, we can write as,

Or,

Similarly, applying the loop rule in ADCBA, we can write as,

Or,

Replacing ‘i’ in eqn.1 using eqn.2, we get,

Or,

Or,

Now i_{1}/i_{2} is,

b)

Given resistances are: 1 Ω,1 Ω,1Ω

Applying Loop rule, we can write,

Or,

And i_{1} will be,

In the next figure,

Let i be the current that passes through the middle branch and hence i_{2}-i will pass through the upper branch, as shown in figure.

By applying loop rule in AFEDA, we can write as,

Or,

Similarly, applying the loop rule in ADCBA, we can write as,

Or,

Replacing ‘i’ in eqn.1 using eqn.2, we get,

Or,

Or,

Now i_{1}/i_{2} is,

c)

Given resistances are: 1 Ω,1 Ω,10Ω

Applying Loop rule, we can write,

Or,

And i_{1} will be,

In the next figure,

Let i be the current that passes through the middle branch and hence i_{2}-i will pass through the upper branch, as shown in figure.

By applying loop rule in AFEDA, we can write as,

Or,

Similarly, applying the loop rule in ADCBA, we can write as,

Or,

Replacing ‘i’ in eqn.1 using eqn.2, we get,

Or,

Or,

Now i_{1}/i_{2} is,

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