Resistivity, conductivity and temperature dependence — practice questions

Question 1 · difficulty L2 · understanding

At room temperature $$(27^{\circ} \mathrm{C})$$, the resistance of a heating element is $$50 \Omega$$. The temperature coefficient of the material is $$2.4 \times 10^{-4}{ }^{\circ} \mathrm{C}^{-1}$$. The temperature of the element, when its resistance is $$62 \Omega$$, is __________$${ }^{\circ} \mathrm{C}$$.

Question 2 · difficulty L2 · understanding

A rectangular parallelopiped is measured as $$1 \mathrm{~cm} \times 1 \mathrm{~cm} \times 100 \mathrm{~cm}$$. If its specific resistance is $$3 \times 10^{-7} ~\Omega \mathrm{m}$$, then the resistance between its two opposite rectangular faces will be ___________ $$\times 10^{-7} ~\Omega$$.

Question 3 · difficulty L2 · understanding

The length of a metallic wire is increased by $$20 \%$$ and its area of cross section is reduced by $$4 \%$$. The percentage change in resistance of the metallic wire is __________.

Question 4 · difficulty L2 · understanding

A hollow cylindrical conductor has length of 3.14 m, while its inner and outer diameters are 4 mm and 8 mm respectively. The resistance of the conductor is $$n\times10^{-3}\Omega$$. If the resistivity of the material is $$\mathrm{2.4\times10^{-8}\Omega m}$$. The value of $$n$$ is ___________.

Question 5 · difficulty L2 · understanding

The length of a given cylindrical wire is increased to double of its original length. The percentage increase in the resistance of the wire will be ____________ %.

Question 6 · difficulty L2 · understanding

A wire of length 25 m and cross-sectional area $5 \mathrm{~mm}^2$ having resistivity of $2 \times 10^{-6} \Omega \mathrm{~m}$ is bent into a complete circle. The resistance between diametrically opposite points will be

• A. $100 \Omega$
• B. $2.5 \Omega$
• C. $12.5 \Omega$
• D. $50 \Omega$

Question 7 · difficulty L2 · understanding

Wheatstone bridge principle is used to measure the specific resistance $$\left(S_1\right)$$ of given wire, having length $$L$$, radius $$r$$. If $$X$$ is the resistance of wire, then specific resistance is ; $$S_1=X\left(\frac{\pi r^2}{L}\right)$$. If the length of the wire gets doubled then the value of specific resistance will be :

• A. $$\frac{S_1}{4}$$
• B. $$2 \mathrm{~S}_1$$
• C. $$\frac{\mathrm{S}_1}{2}$$
• D. $$S_1$$

Question 8 · difficulty L2 · understanding

A wire of resistance $$160 ~\Omega$$ is melted and drawn in a wire of one-fourth of its length. The new resistance of the wire will be

• A. $$640 ~\Omega$$
• B. $$40 ~\Omega$$
• C. $$16 ~\Omega$$
• D. $$10 ~\Omega$$

Question 9 · difficulty L2 · understanding

The resistance of a wire is 5 $$\Omega$$. It's new resistance in ohm if stretched to 5 times of it's original length will be :

• A. 25
• B. 625
• C. 5
• D. 125

Question 10 · difficulty L2 · understanding

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Alloys such as constantan and manganin are used in making standard resistance coils. Reason R: Constantan and manganin have very small value of temperature coefficient of resistance. In the light of the above statements, choose the correct answer from the options given below.

• A. Both A and R are true and R is the correct explanation of A.
• B. Both A and R are true but R is NOT the correct explanation of A.
• C. A is true but R is false.
• D. A is false but R is true.