Question

) The error in measurement of unknown
resistance of X is minimum in a meter
bridge when I = 70 cm, where l is the
distance of null point from one end. If X =
[l/(A-l)]R, find the value of A, where R is
known resistance.
1) 35 cm
3) 140 cm
2) 105 cm
4) 210 cm​

Answer 1

Answer:

correct answer is 140cm

Explanation:

Let, X = 1

because X is minimum measurements

given data :-

I = 70cm

R = 1 ( R. is measure's in Ohm)

then put values in given formula

X = [ I / (A -I ) ] × R

therefore

1 = [ 70 / A- 70 ] × 1

then

A = 140 cm

the correct answer is option (B ) 140 cm

Answer 2

Answer:

The value of A is 3) 140 cm.

Resistance:

• Resistance is defined as the opposition to the flow of electric current.
• It is calculated as $R=\frac{V}{I}$, where R is the resistance, V is the applied voltage, and I is the electric current.
• Resistance of a wire is directly proportional to its length and inversely proportional to its area of cross-section.

Error Measurement:

• Defects in the measurement of physical quantities lead to errors. However, these errors can be reduced in different ways.
• Lesser the error, more is the accuracy in the measurement of a physical quantity.

• The four types of errors are

1. Instrumental error
2. Systematic error
3. Personal error
4. Random error

Explanation:

Given: l=70cm

To find: A

Formula: $X=\frac{l}{(A-l)} R$

Step 1:

The error in unknown resistance X is given to be minimum. Therefore,

$\frac{dX}{X} = 0$ ...(i)

where dX is the error in X

Step 2:

Using the error measurement formulas, we get

$\frac{dX}{X}=[\frac{dl}{l}-\frac{dl}{(A-l)} ]R$ , where dl is the error in l

From equation (i)

$\frac{dX}{X}=[\frac{dl}{l}-\frac{dl}{(A-l)} ]R=0$

Step 3:

$[\frac{dl}{l}-\frac{dl}{(A-l)} ]R=0$

$\frac{dl}{l}-\frac{dl}{(A-l)} = 0$

$\frac{dl}{l}=\frac{dl}{A-l}$

$\frac{1}{l}=\frac{1}{A-l}$

$A-l=l$

$A=2l$

$A=2(70)$

$A=140cm$

Therefore, the value of A in the given meter bridge is 140cm.

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