SATHEE: Current Electricity 1 Question 9

Current Electricity 1 Question 9

9. A copper wire is stretched to make it $0.5$ longer. The percentage change in its electrical resistance, if its volume remains unchanged is

(2019 Main, 9 Jan I)

(a) $2.0$

(b) $1.0$

(d) $2.5$

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Solution:

Electrical resistance of wire of length ’ $l$ ‘, area of cross-section ’ $A$ ’ and resistivity ’ $ρ$ ’ is given as

$R = ρ \frac{l}{A}$

Since we know, volume of the wire is

$V = A \times l$

$∴$ From Eqs. (i) and (ii), we get

$R = o \frac{l^{2}}{V}$

As, the length has been increased to $0.5$ .

$∴$ New length of the wire,

$\begin{aligned} l^{'} & = l + 0.5 & = l + 0.005 l = 1.005 l \end{aligned}$

But $V$ and $ρ$ remains unchanged.

So, new resistance, $R^{'} = \frac{ρ [(1.005) l]^{2}}{V}$

Dividing Eq. (iv) and Eq. (iii), we get

$\frac{R^{'}}{R} = (1.005)^{2}$

$\Rightarrow$ change in the resistance

$\begin{aligned} = \frac{R^{'}}{R} - 1 \times 100 \\ = [(1.005)^{2} - 1] \times 100 = 1.0025 \end{aligned}$

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Current Electricity 1 Question 9

9. A copper wire is stretched to make it $0.5$ longer. The percentage change in its electrical resistance, if its volume remains unchanged is

Solution:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Current Electricity 1 Question 9

9. A copper wire is stretched to make it 0.5 longer. The percentage change in its electrical resistance, if its volume remains unchanged is

Solution:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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9. A copper wire is stretched to make it $0.5$ longer. The percentage change in its electrical resistance, if its volume remains unchanged is