Single Choice

In an aluminum (Al) bar of square cross section, a square hole is drilled and is filled with iron (Fe) as shown in the figure. The electrical resistivities of Al and Fe are $$2.7 \times 10^{-8} \Omega$$ m and $$1.0 \times 10^{-7} \Omega$$ m, respectively. The electrical resistance between the two faces P and Q of the composite bar is

A$$\displaystyle \frac{2475}{64} \mu \Omega$$
B$$\displaystyle \frac{1875}{64}\mu \Omega$$
Correct Answer
C$$\displaystyle \frac{1875}{49} \mu\Omega$$
D$$\displaystyle \frac{2475}{132} \mu\Omega$$

Solution

$$R_{Al}$$ and $$R_{Fe}$$ are parallel to each other.
$$R =\frac{\rho l}{A}$$
Al:
$$Area = 7^2 -2^2 = 45\: mm^2$$
$$\rho = 2.7 \times 10^{-8} \Omega m$$
$$l =50 \: mm$$
Fe:
$$Area = 2^2 = 4\: mm^2$$
$$\rho = 1.0 \times 10^{-7} \Omega m$$
$$l =50 \: mm$$
Substituting values:
$$R_{Al} = 30 \: \mu \Omega$$
$$R_{Fe} = 1250 \: \mu \Omega$$
$$R_{total} = \dfrac{R_{Al} R_{Fe}}{R_{Al} + R_{Fe}} = \dfrac{30 \times 1250}{30 + 1250} = \dfrac{1875}{64}\: \mu \Omega$$

SIMILAR QUESTIONS

Current Electricity

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

Current Electricity

A uniform wire of length $$l$$ and radius $$r$$ has a resistance of $$100\Omega$$. It is recast into a wire of radius $$\dfrac{r}{2}$$. The resistance of new 2 wire will be :

Current Electricity

When $$5V$$ potential difference is applied across a wire length $$0.1\ m$$, the drift speed of electron is 2.5 $$\times 10^{-4} ms^{-1}$$. If the electron density in the wire is 8 $$\times 10^{28} m^{-3}$$, the resistivity of the material is close to

Current Electricity

The resistance of a wire is $$R$$. It is bent at the middle by $$180^{\circ}$$ and both the ends are twisted together to make a shorter wire. The resistance of the new wire is

Current Electricity

The resistance of a 20 cm long wire is 5 $$\Omega$$. The wire is stretched to form a uniform wire of 40 cm length. The resistance now will be :

Current Electricity

If a copper wire is stretched to make its radius decrease by $$0.1$$%, then the percentage increase in its resistance is approximately:

Current Electricity

If a rod has resistance $$4\Omega$$ and if rod is turned as half circle, then the resistance along diameter is

Current Electricity

The resistance if a wire is '$$R$$' ohm. If it is melted and stretched to '$$n$$' times its original length, its new resistance will be:

Current Electricity

A wire of resistance $$4\:\Omega$$ is stretched to double its original length. The resistance of the stretched wire would be

Current Electricity

If the length and area of cross-section of a conductor are doubled, then its resistance will be

Contact Details