Question

In a meter bridge experiment with resistance R1 in left gap and resistance

X in right gap, null point is obtained at 45.5cm from the left end. With a

resistance R2 in left gap and same resistance X in right gap, null point is

obtained at 55.5cm from the left end. Where will the null point be if R1

and R2 are put in series in the left gap and right gap containing X​

Answer 1

Answer:

the null point is 67.56 cm

Answer 2

The null point in the Meter Bridge when R1 and R2 are put in series in the left gap is 66.67cm.

Given:-

Resistance in the left gap in the first case = r1

Resistance in the left gap in the second case = r2

Resistance in the left gap in the third case = r1 + r2

Resistance in the right gap = x

Null Point (l1) = 45.5cm

Null Point (l2) = 55.5cm

Null Point (l3) =?

To Find:-

The null point in the Meter Bridge when R1 and R2 are put in series in the left gap.

Solution:-

We can simply find out the null point in the Meter Bridge when R1 and R2 are put in series in the left gap by using the following procedure.

As

Resistance in the left gap in the first case = r1

Resistance in the left gap in the second case = r2

Resistance in the left gap in the third case = r1 + r2

Resistance in the right gap = x

Null Point (l1) = 45.5cm

Null Point (l2) = 55.5cm

Null Point (l3) =?

According to the formula,

$\frac{resistance \: in \: left \: gap}{resistane \: in \: righ \: gap} = \frac{null \: point}{100 - \: null \: point}$

$\frac{rl}{rr} = \frac{l}{100 - l}$

In Case 1,

$\frac{r1}{x} = \frac{45.5}{100 - 45.5}$

$\frac{r1}{x} = \frac{45.5}{54.5}$

$\frac{r1}{x} = 0.8$

$r1 = 0.8x$

In Case 2,

$\frac{r2}{x} = \frac{55.5}{100 - 55.5}$

$\frac{r2}{x} = \frac{55.5}{44.5}$

$\frac{r2}{x} = 1.2$

$r2 = 1.2x$

In Case 3,

$\frac{r1 + r2}{x} = \frac{l}{100 - l}$

$\frac{0.8x + 1.2x}{x} = \frac{l}{100 - l}$

$\frac{2x}{x} = \frac{l}{100 - l}$

$\frac{l}{100 - l} = 2$

$l = 200 - 2l$

$3l = 200$

$l = \frac{200}{3}$

l = 66.67cm

Hence, The null point in the Meter Bridge when R1 and R2 are put in series in the left gap is 66.67cm.

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