In a potentiometer of one metre length, an unknown emf voltage source is balanced at 60 cm length of potentiometer wire, while a 3 V battery is balanced at 45 cm length. Then the emf of the unknown voltage source is

Question

In a potentiometer of one metre length, an unknown emf voltage source is balanced at 60 cm length of potentiometer wire, while a 3 V battery is balanced at 45 cm length. Then the emf of the unknown voltage source is (A) 3 V (B) 2.25 V (C) 4 V (D) 4.5 V

Tardigrade Admin · Accepted Answer

Let l1 and l2 be the balancing lengths with the cells E1 and E2 respectively, than E1=x l1 and E2=x l2 ⇒ (E1/E2)=(l1/l2) Or (E1/3)=(60/45) ⇒ E=4 V

Q. In a potentiometer of one metre length, an unknown emf voltage source is balanced at $60 c m$ length of potentiometer wire, while a $3 V$ battery is balanced at $45 c m$ length. Then the emf of the unknown voltage source is

3 V

2.25 V

4 V

4.5 V

Let $l_{1}$ and $l_{2}$
be the balancing lengths with the cells
$E_{1}$ and $E_{2}$ respectively, than
$E_{1} = x l_{1}$ and $E_{2} = x l_{2}$
$\Rightarrow \frac{E _{1}}{E _{2}} = \frac{l _{1}}{l _{2}}$
Or $\frac{E _{1}}{3} = \frac{60}{45}$
$\Rightarrow E = 4 V$

Q. In a potentiometer of one metre length, an unknown emf voltage source is balanced at 60cm length of potentiometer wire, while a 3V battery is balanced at 45cm length. Then the emf of the unknown voltage source is

3 V

2.25 V

4 V

4.5 V

Let l1​ and l2​ be the balancing lengths with the cells E1​ and E2​ respectively, than E1​=xl1​ and E2​=xl2​ ⇒E2​E1​​=l2​l1​​ Or 3E1​​=4560​ ⇒E=4V

Q. In a potentiometer of one metre length, an unknown emf voltage source is balanced at $60 c m$ length of potentiometer wire, while a $3 V$ battery is balanced at $45 c m$ length. Then the emf of the unknown voltage source is

Let $l_{1}$ and $l_{2}$
be the balancing lengths with the cells
$E_{1}$ and $E_{2}$ respectively, than
$E_{1} = x l_{1}$ and $E_{2} = x l_{2}$
$\Rightarrow \frac{E _{1}}{E _{2}} = \frac{l _{1}}{l _{2}}$
Or $\frac{E _{1}}{3} = \frac{60}{45}$
$\Rightarrow E = 4 V$