Question 323: Current Electricity

Question

A potentiometer PQ is set up to compare two resistances as shown in the figure. The ammeter A in the circuit reads 1.0 A when two way key K3  is open. The balance point is at a length $$\ell $$1  cm from P when two way key K3  is plugged in between 2 and 1, while the balance point is at a length $$\ell $$2  cm from P when key K3  is plugged in between 3 and 1. The ratio of two resistances $${{{R_1}} \over {{R_2}}}$$,  is  found to be :

Accepted Answer

When key K
3
is plugged in between 1 and 2,
V
1
= iR
1
= x$$l$$
1
. . . . . (1)
When key K
3
is plugged in between 3 and 1,
V
2
= i(R
1
+ R
2
) = x$$l$$
2
. . . . (2)
On dividing (1) and (2),
$${{{R_1}} \over {{R_1} + {R_2}}} = {{{l_1}} \over {{l_2}}}$$
$$ \Rightarrow $$$$\,\,\,$$ $${{{R_1}} \over {\left( {R{}_1 + {R_2}} \right) - {R_1}}}$$ = $${{{l_1}} \over {{l_2} - {l_1}}}$$
$$ \Rightarrow $$$$\,\,\,$$ $${{{R_1}} \over {{R_2}}}$$ = $${{{l_1}} \over {{l_2} - {l_1}}}$$

Answer

$${{{l_1}} \over {{l_1} + {l_2}}}$$

Answer

$${{{l_2}} \over {{l_2} - {l_1}}}$$

Answer

$${{{l_1}} \over {{l_1} - {l_2}}}$$

Answer

$${{{l_1}} \over {{l_2} - {l_1}}}$$

Current Electricity

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