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1

AIEEE 2004

MCQ (Single Correct Answer)
A material $$'B'$$ has twice the specific resistance of $$'A'.$$ A circular wire made of $$'B'$$ has twice the diameter of a wire made of $$'A'$$. Then for the two wires to have the same resistance, the ratio $${l \over B}/{l \over A}$$ of their respective lengths must be
A
$$1$$
B
$${l \over 2}$$
C
$${l \over 4}$$
D
$$2$$

Explanation

$${\rho _B} = 2{\rho _A}$$

$${d_B} = 2{d_A}$$

$${R_B} = {R_A} \Rightarrow {{{\rho _B}{\ell _B}} \over {{A_B}}} = {{{P_A}{\ell _A}} \over {{A_A}}}$$

$$\therefore$$ $${{{\ell _B}} \over {{\ell _A}}} = {{{\rho _A}} \over {{\rho _B}}} \times {{d_B^2} \over {d_A^2}}$$ $$ = {{{\rho _A}} \over {2{\rho _A}}} \times {{4d_d^2} \over {d_A^2}} = 2$$
2

AIEEE 2004

MCQ (Single Correct Answer)
The Kirchhoff's first law $$\left( {\sum i = 0} \right)$$ and second law $$\left( {\sum iR = \sum E} \right),$$ where the symbols have their usual meanings, are respectively based on
A
conservation of charge, conservation of momentum
B
conservation of energy, conservation of charge
C
conservation of momentum, conservation of charge
D
conservation of charge, conservation of energy

Explanation

NOTE : Kirchhoff's first law is based on conservation of charge and Kirchhoffs second law is based on conservation of energy.
3

AIEEE 2004

MCQ (Single Correct Answer)
The thermo $$emf$$ of a thermocouple varies with temperature $$\theta $$ of the hot junction as $$E = a\theta + b{\theta ^2}$$ in volts where the ratio $$a/b$$ is $${700^ \circ }C.$$ If the cold junction is kept at $${0^ \circ }C,$$ then the neutral temperature is
A
$${1400^ \circ }C$$
B
$${350^ \circ }C$$
C
$${700^ \circ }C$$
D
No neutral temperature is possible for this termocouple.

Explanation

Neutral temperature is the temperature of a hot junction at which $$E$$ is maximum.

$$ \Rightarrow {{dE} \over {d\theta }} = 0$$

or $$a + 2b\theta = 0 \Rightarrow \theta = {{ - a} \over {2b}} = - 350$$

Neutral temperature can never be negative hence no $$\theta $$ is possible.
4

AIEEE 2004

MCQ (Single Correct Answer)
The electrochemical equivalent of a metal is $${3.35109^{ - 7}}$$ $$kg$$ per Coulomb. The mass of the metal liberated at the cathode when a $$3A$$ current is passed for $$2$$ seconds will be
A
$$6.6 \times {10^{57}}/kg$$
B
$$9.9 \times {10^{ - 7}}\,kg$$
C
$$19.8 \times {10^{ - 7}}\,kg$$
D
$$1.1 \times {10^{ - 7}}\,kg$$

Explanation

The mass liberated $$m,$$ electrochemical equivalent of a metal $$Z,$$ are related as $$m = Zit$$

$$ \Rightarrow m = 3.3 \times {10^{ - 7}} \times 3 \times 2$$

$$ = 19.8 \times {10^{ - 7}}\,kg$$

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