Heating Effect of Current and Electrical Measuring Instruments | Physics JEE previous year questions with Solutions

Q 1 :

The value of unknown resistance (x) for which the potential between B and D will be zero in the arrangement shown, is [2024]

$6 Ω$
$9 Ω$
$42 Ω$
$3 Ω$

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(1)

Potential difference between B and D will be zero in a balanced

Wheatstone Bridge

In case of balanced Wheatstone Bridge,

$\frac{V_{A B}}{V_{A D}} = \frac{V_{B C}}{V_{C D}} \Rightarrow \frac{12}{6 + x} = \frac{0.5}{0.5} \Rightarrow x = 6 Ω$

Q 2 :

The resistance per centimeter of a meter bridge wire is r, with $X Ω$ resistance in left gap. Balancing length from left end is at 40 cm with $25 Ω$ resistance in right gap. Now the wire is replaced by another wire of $2 r$ resistance per centimeter. The new balancing length for same settings will be at [2024]

20 cm
10 cm
80 cm
40 cm

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(4)

$\frac{25}{r ℓ_{2}} = \frac{X}{r ℓ_{1}}$ ...(i)

$\frac{25}{2 r ℓ'_{2}} = \frac{X}{2 r ℓ'_{1}}$ ...(ii)

From (i) and (ii) $ℓ'_{2} = ℓ_{2} = 40 c m$

Q 3 :

To measure the temperature coefficient of resistivity $α$ of a semiconductor, an electrical arrangement shown in the figure is prepared. The arm BC is made up of the semiconductor. The experiment is being conducted at 25 °C and resistance of the semiconductor arm is 3 $m Ω$ . Arm BC is cooled at a constant rate of 2° C/s. If the galvanometer G shows no deflection after 10 s, then $α$ is [2024]

$- 1 \times 10^{- 2}$ ${}^{o}{C^{- 1}}$
$- 2 \times 10^{- 2}$ ${}^{o}{C^{- 1}}$
$- 2.5 \times 10^{- 2}$ ${}^{o}{C^{- 1}}$
$- 1.5 \times 10^{- 2}$ ${}^{o}{C^{- 1}}$

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(1)

For no. deflection $= \frac{0.8}{1} = \frac{R}{3}$

$R = 2.4 m Ω$

$Δ R = R α Δ T$

$\Rightarrow α = \frac{Δ R}{R Δ T} = \frac{- 0.6}{3 \times 20} = - 10^{- 2}$ ${}^{o}{C^{- 1}}$

Q 4 :

In a metre-bridge when a resistance in the left gap is $2 Ω$ and unknown resistance in the right gap, the balance length is found to be 40 cm. On shunting the unknown resistance with $2 Ω$ , the balance length changes by [2024]

22.5 cm
20 cm
62.5 cm
65 cm

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(1)

Given for $l_{1} = 40$ cm
$\frac{R}{l_{1}} = \frac{X}{l_{2}} \Rightarrow \frac{2}{40} = \frac{X}{60}$

$x = 3 Ω$

After shunting

$R_{eq} = \frac{2 \times 3}{3 + 2} = \frac{6}{5} Ω$

$\frac{R}{l} = \frac{R_{eq}}{100 - l} \Rightarrow \frac{2}{l} = \frac{6}{5 (100 - l)}$

$\Rightarrow 10 (100 - l) = 6 l$

$500 - 5 l = 3 l$

$500 = 8 l$

$l = \frac{500}{8} = \frac{125}{2} = 62.5 cm$

Balance length change

by $= 62.5 - 40 = 22.5 cm$

Q 5 :

In a metre bridge experiment, the balance point is obtained if the gaps are closed by 2 $Ω$ and 3 $Ω$ . A shunt of $X Ω$ is added to the 3 $Ω$ resistor to shift the balancing point by 22.5 cm. The value of $X$ is __________. [2023]

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(2)

$\frac{2}{(\frac{3 x}{3 + x})} = \frac{40 + 22.5}{60 - 22.5} = \frac{62.5}{37.5} = \frac{5}{3}$

$\frac{6}{5} = \frac{3 x}{3 + x} \Rightarrow 6 + 2 x = 5 x \Rightarrow x = 2$

Q 6 :

When two resistances $R_{1}$ and $R_{2}$ are connected in series and introduced into the left gap of a metre bridge and a resistance of $10 Ω$ is introduced into the right gap, a null point is found at 60 cm from the left side. When $R_{1}$ and $R_{2}$ are connected in parallel and introduced into the left gap, a resistance of $3 Ω$ is introduced into the right gap to get a null point at 40 cm from the left end. The product of $R_{1} R_{2}$ is ________ $Ω^{2}$ . [2023]

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(30)

$\frac{R_{1} + R_{2}}{10} = \frac{60}{40} = \frac{3}{2} \Rightarrow R_{1} + R_{2} = 15$

$Now \frac{R_{1} R_{2}}{(R_{1} + R_{2}) \times 3} = \frac{40}{60} = \frac{2}{3} \Rightarrow R_{1} R_{2} = 30$

Q 7 :

A meter bridge with two resistances $R_{1}$ and $R_{2}$ as shown in the figure was balanced (null point) at 40 cm from the point P. The null point changed to 50 cm from the point P when $16 Ω$ resistance is connected in parallel to $R_{2}$ . The values of resistances $R_{1}$ and $R_{2}$ are _______. [2026]

[IMAGE 43]

$R_{2} = 4 Ω, R_{1} = \frac{4}{3} Ω$
$R_{2} = 12 Ω, R_{1} = \frac{12}{3} Ω$
$R_{2} = 16 Ω, R_{1} = \frac{16}{3} Ω$
$R_{2} = 8 Ω, R_{1} = \frac{16}{3} Ω$

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(4)

Topic Question Set

Q 1 :

The value of unknown resistance (x) for which the potential between B and D will be zero in the arrangement shown, is [2024]

Q 4 :

In a metre-bridge when a resistance in the left gap is $2 Ω$ and unknown resistance in the right gap, the balance length is found to be 40 cm. On shunting the unknown resistance with $2 Ω$ , the balance length changes by [2024]

Q 5 :

In a metre bridge experiment, the balance point is obtained if the gaps are closed by 2 $Ω$ and 3 $Ω$ . A shunt of $X Ω$ is added to the 3 $Ω$ resistor to shift the balancing point by 22.5 cm. The value of $X$ is __________. [2023]

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