Electric Resistance and Simple Circuits | Physics JEE previous year questions with Solutions

Q 1 :
The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are $8 Ω$ and $10 Ω$ respectively. After inserting in a hot bath of temperature 400°C, the resistance of platinum wire is : [2024]

$8 Ω$
$10 Ω$
$16 Ω$
$2 Ω$

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(C) Given, $R_{0} = 8 Ω$ and $R_{100} = 10 Ω$

$∴$ $R_{100} = R_{0} (1 + α ∆ T)$

$∴$ $10 = 8 (1 + α \times 100) \Rightarrow 100 α = \frac{1}{4}$

Also, $R_{400} = R_{0} (1 + α ∆ T)$

$∴$ $R_{400} = 8 (1 + 400 α) = 8 (1 + 1) = 16 Ω$

Q 2 :
An electric toaster has resistance of $60 Ω$ at room temperature (27°C). The toaster is connected to a 220 V supply. If the current flowing through it reaches 2.75 A, the temperature attained by toaster is around

(if $α = 2 \times 10^{- 4} / {}^{o}C$ ) [2024]

694°C
1235°C
1694°C
1667°C

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(C) $R_{n e w} = V / I = 80 Ω$

$R_{n e w} = R_{o l d} [1 + α ∆ T]$

$80 = 60 [1 + 2 \times 10^{- 4} ∆ T]$

$∆ T = 1666.67$

$T - 27 = 1666.67$

$T = 1693.66 = 1694^{o} C$

Q 3 :
Two conductors have the same resistances at $0^{o} C$ but their temperature coefficients of resistance are $α_{1}$ and $α_{2}$ . The respective temperature coefficients for their series and parallel combinations are [2024]

$α_{1} + α_{2}, \frac{α_{1} + α_{2}}{2}$
$\frac{α_{1} + α_{2}}{2}, \frac{α_{1} + α_{2}}{2}$
$\frac{α_{1} + α_{2}}{2}, α_{1} + α_{2}$
$α_{1} + α_{2}, \frac{α_{1} α_{2}}{α_{1} + α_{2}}$

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(B) Series: $R_{e q} = R_{1} + R_{2}$

$2 R (1 + α_{e q} ∆ θ) = R (1 + α_{1} ∆ θ) + R (1 + α_{2} ∆ θ)$

$2 R (1 + α_{e q} ∆ θ) = 2 R + (α_{1} + α_{2}) R ∆ θ$

$\Rightarrow α_{e q} = \frac{α_{1} + α_{2}}{2}$

Parallel: $\frac{1}{R_{e q}} = \frac{1}{R_{1}} + \frac{1}{R_{2}}$

$\frac{1}{\frac{R}{2} (1 + α_{e q} ∆ θ)} = \frac{1}{R (1 + α_{1} ∆ θ)} + \frac{1}{R (1 + α_{2} ∆ θ)}$

$\frac{2}{1 + α_{e q} ∆ θ} = \frac{1}{1 + α_{1} ∆ θ} + \frac{1}{1 + α_{2} ∆ θ}$

$\frac{2}{1 + α_{e q} ∆ θ} = \frac{1 + α_{2} ∆ θ + 1 + α_{1} ∆ θ}{(1 + α_{1} ∆ θ) (1 + α_{2} ∆ θ)}$

$2 [(1 + α_{1} ∆ θ) (1 + α_{2} ∆ θ)]$

$= [2 + (α_{1} + α_{2}) ∆ θ] [1 + α_{e q} ∆ θ]$

$2 [1 + α_{1} ∆ θ + α_{2} ∆ θ + α_{1} α_{2} ∆ θ]$

$= 2 + 2 α_{e q} ∆ θ + (α_{1} + α_{2}) ∆ θ + α_{e q} (α_{1} + α_{2}) ∆ θ^{2}$

Neglecting small terms

$2 + 2 (α_{1} + α_{2}) ∆ θ = 2 + 2 α_{e q} ∆ θ + (α_{1} + α_{2}) ∆ θ$

$(α_{1} + α_{2}) ∆ θ = 2 α_{e q} ∆ θ \Rightarrow α_{e q} = \frac{α_{1} + α_{2}}{2}$

Q 4 :
Two wires A and B are made up of the same material and have the same mass. Wire A has radius of 2.0 mm and wire B has radius of 4.0 mm. The resistance of wire B is 2 $Ω$ . The resistance of wire A is _______ $Ω$ . [2024]

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(32) Given: $r_{A} = 2 \times 10^{- 3} m,$ $r_{B} = 4 \times 10^{- 3} m,$ $R_{B} = 2 Ω$

We know $R = \frac{ρ l}{A}$

$\frac{R_{A}}{R_{B}} = \frac{ρ_{A} l_{A}}{A_{A}} \times \frac{A_{B}}{ρ_{B} l_{B}} = \frac{l_{A}}{l_{B}} \frac{A_{B}}{A_{A}}$ ...(i)

The volume of wire remains constant, $V_{A} = V_{B}$

$l_{A} A_{A} = l_{B} A_{B} \Rightarrow \frac{l_{A}}{l_{B}} = \frac{A_{B}}{A_{A}}$ ...(ii)

from equation (i) and equation (ii)

$R_{A} = R_{B} {(\frac{A_{B}}{A_{A}})}^{2} = 2 {(\frac{π \times {(4 \times 10^{- 3})}^{2}}{π \times {(2 \times 10^{- 3})}^{2}})}^{2} = 2 \times 16 = 32 Ω$

$\Rightarrow R_{A} = 32 Ω$

Q 5 :
A wire of resistance R and radius r is stretched till its radius became r/2. If new resistance of the stretched wire is x R. then value of x is _______ . [2024]

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(16) We know $R = \frac{ρ l}{A} \Rightarrow R \propto \frac{l}{r^{2}}$

As we stretch the wire, its length will increase but its radius will decrease keeping the volume constant.

$V_{i} = V_{f} \Rightarrow π r^{2} l = π \frac{r^{2}}{4} l_{f} \Rightarrow l_{f} = 4 l$

$\frac{R_{n e w}}{R_{o l d}} = (\frac{4 l}{\frac{r^{2}}{4}}) \frac{r^{2}}{l} = 16$

$R_{n e w} = 16 R$

$∴ x = 16$

Q 6 :
Resistance of a wire at 0°C, 100°C and t °C is found to be 10 $Ω$ , 10.2 $Ω$ and 10.95 $Ω$ respectively. The temperature t in Kelvin scale is _______ . [2024]

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(748) $R = R_{0} (1 + α ∆ T) \Rightarrow \frac{∆ R}{R_{0}} = α ∆ T$

Case-I:

$\frac{10.2 - 10}{10} = α (100 - 0)$ ...(i)

Case-II:

$\frac{10.95 - 10}{10} = α (t - 0)$ ...(ii)

$\Rightarrow \frac{t}{100} = \frac{0.95}{0.2} = 475^{o} C \Rightarrow t = 475 + 273 = 748 K$

Q 7 :
At room temperature (27°C) the resistance of a heating element is 50 $Ω$ . The temperature coefficient of the material is $2.4 \times 10^{- 4^{o}}$ $C^{- 1}$ . The temperature of the element, when its resistance is 62 $Ω$ , is ______ ${}^{o}C$ . [2024]

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(1027) $R_{0} = 50 Ω;$ $α = 2.4 \times 10^{- 4^{o}}$ $C^{- 1};$ $R = 62 Ω$

$R = R_{0} (1 + α ∆ T)$

$62 = 50 (1 + 2.4 \times 10^{- 4} \times ∆ T)$

$1.24 = 1 + 2.4 \times 10^{- 4} \times ∆ T$

$0.24 = 2.4 \times 10^{- 4} \times ∆ T$

$∆ T = \frac{0.24}{2.4 \times 10^{- 4}} = 1000$

$∴$ Final temperature, $T_{f} = 1000 + 27 = 1027^{o} C$

Topic Question Set

Q 1 :
The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are $8 Ω$ and $10 Ω$ respectively. After inserting in a hot bath of temperature 400°C, the resistance of platinum wire is : [2024]

Q 2 :
An electric toaster has resistance of $60 Ω$ at room temperature (27°C). The toaster is connected to a 220 V supply. If the current flowing through it reaches 2.75 A, the temperature attained by toaster is around

(if $α = 2 \times 10^{- 4} / {}^{o}C$ ) [2024]

Q 3 :
Two conductors have the same resistances at $0^{o} C$ but their temperature coefficients of resistance are $α_{1}$ and $α_{2}$ . The respective temperature coefficients for their series and parallel combinations are [2024]

Q 4 :
Two wires A and B are made up of the same material and have the same mass. Wire A has radius of 2.0 mm and wire B has radius of 4.0 mm. The resistance of wire B is 2 $Ω$ . The resistance of wire A is _______ $Ω$ . [2024]

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Q 5 :
A wire of resistance R and radius r is stretched till its radius became r/2. If new resistance of the stretched wire is x R. then value of x is _______ . [2024]

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Q 6 :
Resistance of a wire at 0°C, 100°C and t °C is found to be 10 $Ω$ , 10.2 $Ω$ and 10.95 $Ω$ respectively. The temperature t in Kelvin scale is _______ . [2024]

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Q 7 :
At room temperature (27°C) the resistance of a heating element is 50 $Ω$ . The temperature coefficient of the material is $2.4 \times 10^{- 4^{o}}$ $C^{- 1}$ . The temperature of the element, when its resistance is 62 $Ω$ , is ______ ${}^{o}C$ . [2024]

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Topic Question Set

Q 1 : The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are 8Ω and 10Ω respectively. After inserting in a hot bath of temperature 400°C, the resistance of platinum wire is : [2024]

Q 2 : An electric toaster has resistance of 60Ω at room temperature (27°C). The toaster is connected to a 220 V supply. If the current flowing through it reaches 2.75 A, the temperature attained by toaster is around (if α=2×10-4/Co) [2024]

Q 3 : Two conductors have the same resistances at 0oC but their temperature coefficients of resistance are α1 and α2. The respective temperature coefficients for their series and parallel combinations are [2024]

Q 4 : Two wires A and B are made up of the same material and have the same mass. Wire A has radius of 2.0 mm and wire B has radius of 4.0 mm. The resistance of wire B is 2 Ω. The resistance of wire A is _______ Ω. [2024]

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Q 5 : A wire of resistance R and radius r is stretched till its radius became r/2. If new resistance of the stretched wire is x R. then value of x is _______ . [2024]

0%

Q 6 : Resistance of a wire at 0°C, 100°C and t °C is found to be 10 Ω, 10.2 Ω and 10.95 Ω respectively. The temperature t in Kelvin scale is _______ . [2024]

0%

Q 7 : At room temperature (27°C) the resistance of a heating element is 50 Ω. The temperature coefficient of the material is 2.4×10-4o C-1. The temperature of the element, when its resistance is 62 Ω, is ______ Co. [2024]

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Q 1 :
The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are $8 Ω$ and $10 Ω$ respectively. After inserting in a hot bath of temperature 400°C, the resistance of platinum wire is : [2024]

Q 2 :
An electric toaster has resistance of $60 Ω$ at room temperature (27°C). The toaster is connected to a 220 V supply. If the current flowing through it reaches 2.75 A, the temperature attained by toaster is around

(if $α = 2 \times 10^{- 4} / {}^{o}C$ ) [2024]

Q 3 :
Two conductors have the same resistances at $0^{o} C$ but their temperature coefficients of resistance are $α_{1}$ and $α_{2}$ . The respective temperature coefficients for their series and parallel combinations are [2024]

Q 4 :
Two wires A and B are made up of the same material and have the same mass. Wire A has radius of 2.0 mm and wire B has radius of 4.0 mm. The resistance of wire B is 2 $Ω$ . The resistance of wire A is _______ $Ω$ . [2024]

Q 5 :
A wire of resistance R and radius r is stretched till its radius became r/2. If new resistance of the stretched wire is x R. then value of x is _______ . [2024]

Q 6 :
Resistance of a wire at 0°C, 100°C and t °C is found to be 10 $Ω$ , 10.2 $Ω$ and 10.95 $Ω$ respectively. The temperature t in Kelvin scale is _______ . [2024]

Q 7 :
At room temperature (27°C) the resistance of a heating element is 50 $Ω$ . The temperature coefficient of the material is $2.4 \times 10^{- 4^{o}}$ $C^{- 1}$ . The temperature of the element, when its resistance is 62 $Ω$ , is ______ ${}^{o}C$ . [2024]