Factors Affecting Resistance & How They Affect

Q.

State three factors on which the resistance of a wire depends. Explain how does the resistance depend on the factors stated by you.

Q.

How is the resistance of a wire affected if its (a) length is doubled, (b) radius is doubled?

Q.

A metal wire of resistance $6\Omega$ is stretched so that its length is increased to twice of original length. Calculate its new resistance.

Q.

Why are copper and aluminium wires usually employed for electricity transmission?

1. 2%

2. 1%

3. 0.2%

4. 1%

Q. Which of the following are the factors affecting resistance of a conductor?

1. Material of the conductor
2. Dimensions of the conductor
3. Temperature of the conductor
4. All of the above.

Q.

If the radius of the wire of resistance R is made n times, its mass remaining constant, then its new resistance will be

1. $n^{2}R$

2. $n^{4}R$

3. $\frac{R}{n^2}$

4. $\frac{R}{n^4}$

Q.

When a copper wire is stretched, how does the resistance between its ends change?

1. Increases

2. Decreases

3. Remains unchanged

4. None of the above

Q.

Two resistors of the same material and cross section area but different lengths $L_1$ & $L_2$ have their resistances in the ratio

1. L1xL2/(L1+L2)

2. L1+L2

3. 1/L1 + 1/L2

4. L1-L2

Q.

1. Write the formula for resistance of a wire of length L and cross-section A.
2. A piece of wire is redrawn by pulling it until its length is doubled. Compare the new
resistance with the original value.
3. How many 176$\Omega$ resistors (in parallel) are required to carry 5 A in 220 V line? [5 MARKS]

Q.

If a metallic wire of resistance R is melted and recast to half of its length, the new resistance of the wire will be?

1. $\frac{R}{4}$
   
2. $\frac{R}{2}$
   
3. R
   
4. 2R

Q.

The resistance of 100 m long copper wire with diameter 1 mm is = ___ ohms.

Q.

A metallic wire of resistance R is melted and recast to half of its original length while maintaining the original volume. What will the new resistance of the wire be?

1. $\frac{R}{4}$
   

2. $\frac{R}{2}$
   

3. 4R
   

4. 2R

Q. A wire of resistance $100$ $\Omega$ is doubled on itself. The new resistance is

1. $100$ ohms
2. $200$ ohms
3. $300$ ohms
4. $400$ ohms

Q.

Define one ohm

Q. Two copper wires whose masses are 8 and 12 gm have lengths in the ratio $3:4$. Their resistances are in the ratio.

1. $16:9$
2. $4:9$
3. $27:32$
4. $27:128$

Q.

$1kg$ piece of copper is drawn into a wire $1m{m}^2$ thick, and another $1kg$ copper piece into a wire $2m{m}^2$ thick. Ratio of resistances respectively is

1. $2:1$

2. $4:1$

3. $16:1$

4. $8:1$

Q. A letter 'A' is constructed of a uniform wire of resistance $1ohm/cm$. The sides of the letter are $20cm$ long and the cross piece in the middle is $10cm$ long while the vertex angle is ${60}^o$. The resistance of the letter between the two ends of the legs is:

1. $\frac{40}{3}\Omega$
2. $\frac{80}{3}\Omega$
3. $40\Omega$
4. $10\Omega$

Q.

The length and radius of a wire are $l$ and $r$ respectively, and its resistance is $R$. If the length and radius are doubled, then its new resistance _____

1. remains same

2. is doubled

3. is $\frac{R}{2}$

4. is $\frac{R}{4}$

Q.

An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the lengths and radii of the wires are in the ratio $\frac{4}{3}$ and $\frac{2}{3}$, then the ratio of the currents passing through the wires will be :

1. $\frac{1}{3}$
2. $\frac{8}{9}$
3. $3$
4. $2$

Q. An aluminum rod and a copper rod are taken such that their lengths are same and their resistances are also same. The specific resistance of copper is half that of aluminum, but its density is three times that of aluminum. The ratio of the mass of aluminum rod and that of copper rod will be

1. $\frac{1}{6}$
2. $\frac{2}{3}$
3. $\frac{1}{3}$
4. $6$

Q. The areas of cross section of two wires of the same material are in the ratio $1:2$ and their lengths are in the ratio $2:1$. If their ends have the same potential differences then currents through them will be in the ratio of

1. $1:2$
2. $4:1$
3. $2:1$
4. $1:4$

Q. Four wires made of same material have different lengths and radii. The wire having more resistance in the following is

1. l = 50 cm r = 2 mm
2. l = 100 cm r = 1 mm
3. l = 100 cm r = 1/2 mm
4. l = 50 cm r = 1/2 mm

Q. Wires A and B have resistivities ${\rho }_A$ and ${\rho }_B$, $({\rho }_B=2{\rho }_A)$ and have lengths $l_A$ and $l_B$. If the diameter of the wire B is twice that of A and the two wires have same resistance, then $\frac{l_B}{l_A}$ is:

1. $1$
2. $2$
3. $1/2$
4. $1/4$

Q. Two wires have their lengths in the ratio $1:3$ diameters in the ratio $2:3$ and their materials have specific resistances in the ratio $2:1$. Then the ratio of their resistances is :

1. $1:3$
2. $3:1$
3. $3:2$
4. $2:3$

Q. A metallic wire of resistance $20$ ohm stretched until its length is doubled. Its resistance is

1. $80\Omega$
   
2. $40\Omega$
3. $60\Omega$
4. $20\Omega$

Q. An electrical cable of copper has just one wire of radius 9 mm. Its resistance is 5 ohm. This single copper wire of the cable is replaced by 6 different well insulated copper wires each of radius 3 mm. If now the resistances are connected in parallel, the total resistance of the cable will now be equal to:

1. 7.5 ohm
2. 45 ohm
3. 90 ohm
4. 270 ohm

Q. For which of the following substances, resistance decreases with increase in temperature?
(a) copper (b) mercury (c) carbon (d) platinum.

Q. You have a metal wire of length $1000m$, radius of $0.7mm$ andresistivity of the metal is given as $153.86\times {10}^{-6}\Omega$-m. Find the resistance of the wire.

1. $100k\Omega$
2. $40k\Omega$
3. $18k\Omega$
4. $250k\Omega$

Q. The following table gives the lengths of three copper rods and their diameters. The resistances between the two ends of the rods arranged in ascending order is

Rod	Length	Diameter
A	$l$	d
B	$2l$	$d/2$
C	$l/2$	d
D	$l$	$d/2$

1. C, A, B, D
2. C, A, D, B
3. C, B, D, A
4. A, B, C, D

Q. Two wires are as follows. The resistivities, lengths and radii are in the ratio $2:3$, $3:5$ and $2:7$ respectively. Their resistances are in the ratio of

1. $7:2$
2. $49:10$
3. $2:4$
4. $1:2$