Q: What length of copper wire of resistivity 1.7\, \times \, 10^{-8}\,\Omega\,m and radius 1 mm is required so that its resistance is 1\, \Omega ?

\textbf{Step 1: The resistance of wire is expressed as} R=\dfrac { \rho L }{ A } ....(1) Given, R = 1 \Omega , The area of cross section, A= \pi { r }^{ 2 }=3.14\times { 0.001 }^{ 2 }=3.14\times { 10 }^{ -6 } .Resistivity \rho = 1.7\times {10}^{-8} ohm-meter \textbf{Step 2: Putting above values in equation} (1) We get 1=\dfrac { 1.7\times { 10 }^{-8} \times L }{ 3.14\times { 10 }^{ -6 } } \Rightarrow L=\dfrac { 1\times 3.14\times { 10 }^{ -6 } }{ 1.7\times { 10 }^{ -8 } } =\dfrac { \quad 3.14\times { 10 }^{ -6 } }{ 1.7\times { 10 }^{ -8 } } =1.847\times { 10 }^2 m .Therefore, the length of the wire is 184.7 meters.Hence, Option A is correct.

Q: State Ohms law?

\textbf{Ohm's law:} It states that the current (I) flowing through a conductor is directly proportional to the potential difference (V) across the conductor provided all physical conditions and temperature remains constant i.e. I\propto V \therefore\ \ V = IR Where R is the resistance of the conductor. \textbf{Alternative form of Ohm's Law: } It states that, the current density (J) through a conductor is proportional to the Electric Field (E) across it. J = \sigma E Where \sigma is the conductivity of the conductor.

Question 1

A wire of length L and resistance R is stretched so that the length is doubled and area of cross section halved. How will (i) resistance change and (ii) resistivity change.

Accepted Answer

\Rightarrow  Length  (l)  is doubled & Area of cross section (A) is halved. l  becomes  2l  & A becomes  \frac{A}{2} R = P\frac{L}{A} now take  l = 2l,A = \frac{A}{2} R = \frac{{P2l}}{{A/2}} = 4P\frac{L}{A} \Rightarrow 4R Resistance becomes 4 times1) Resistivity does not depend on its length 02 Area.Hence, it does not change.

Question 2

Two wires of same material have lengths  L  and  2L  cross-sectional areas  4A  and  A  respectively. The ratio of their resistances would be

Accepted Answer

As R=\cfrac { ho l }{ A } R\propto \cfrac { l }{ A } \cfrac { { R }_{ 1 } }{ { R }_{ 2 } } =\cfrac { { l }_{ 1 } }{ { A }_{ 1 } } imes \cfrac { { A }_{ 2 } }{ { l }_{ 2 } } \cfrac { { R }_{ 1 } }{ { R }_{ 2 } } =\cfrac { L }{ 4A } imes \cfrac { A }{ 2L } =1:8

⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎡ l_{1} = L l_{2} = 2 L A_{1} = 4 A A_{2} = A ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎤

Question 3

(a) State Ohm's law.(b) Describe an experiment to verify this law.

Accepted Answer

(a)The potential difference across the ends of a given metallic wire in an electric circuit is directly proportional to the current flowing through it, provided its temperature remains the same. This is called Ohm’s law.(b) Experiment to verify Ohm's law:Set up a circuit as shown in figure shown, consisting of a nichrome wire XY of length, say  0.5 m , an ammeter, a voltmeter and four cells of  1.5 V  each. First use only one cell as the source in the circuit. Note the reading in the ammeter  I , for the current and reading of the voltmeter  V  for the potential difference across the nichrome wire XY in the circuit. Tabulate them in a table. Next connect two cells in the circuit and note the respective readings of the ammeter and voltmeter for the values of current through the nichrome wire and potential difference across the nichrome wire. Repeat the above steps using three cells and then four cells in the circuit separately. Calculate the ratio of V to I for each pair of potential difference V and current I. In this experiment, we will find that approximately the same value for  \cfrac {V  }{  I}   is obtained in each case. Thus the V–I graph is a straight line that passes through the origin of the graph, as shown in the figure. Thus, V/I is a constant ratio, which verifies Ohm's law.

Question 4

State and explain Ohm's law.

Accepted Answer

Statement:  The electric current passing through a conductor is directly proportional to the potential difference across its ends provided temperature and other physical conditions remain constant. Explanation: Current is directly proportional to voltage loss through a resistor. That is, if the current doubles, then so does the voltage. To make a current flow through a resistance there must be a voltage across that resistance. Ohm's Law shows the relationship between the voltage (V), current (I) and resistance (R). V\propto I  or  I\propto V\Rightarrow V = IR .

Question 5

The voltage - current  (V-I)  graph of a metallic conductor at two different temperature  T_{1}  and  T_{2}  is shown below. At which temperature is the resistance higher?

Accepted Answer

The mathematical expression for Ohm's law is:                                    V=IR Thus, graph between V versus I gives a straight line with slope R.Since, slope at  {T_{2}}  is more than slope at  {T_{1}} . For metallic conductors, resistance is directly proportional to temperature. Thus, resistance is higher at  {T_{2}}

Question 6

What length of copper wire of resistivity  1.7\, 	imes \, 10^{-8}\,\Omega\,m  and  radius 1 mm is required so that its resistance is  1\, \Omega ?

Accepted Answer

extbf{Step 1: The resistance of wire is expressed as}    R=\dfrac { ho L }{ A }                                         ....(1) Given,  R = 1 \Omega , The area of cross section,   A= \pi { r }^{ 2 }=3.14	imes { 0.001 }^{ 2 }=3.14	imes { 10 }^{ -6 } .Resistivity  ho = 1.7	imes {10}^{-8}  ohm-meter 	extbf{Step 2: Putting above values in equation}   (1) We get  1=\dfrac { 1.7	imes { 10 }^{-8} 	imes L }{ 3.14	imes { 10 }^{ -6 } }    \Rightarrow L=\dfrac { 1	imes 3.14	imes { 10 }^{ -6 } }{ 1.7	imes { 10 }^{ -8 } } =\dfrac { \quad 3.14	imes { 10 }^{ -6 } }{ 1.7	imes { 10 }^{ -8 } } =1.847	imes { 10 }^2 m .Therefore, the length of the wire is 184.7 meters.Hence, Option A is correct.

Question 7

State Ohms law?

Accepted Answer

extbf{Ohm's law:}  It states that the current (I)  flowing through a conductor is directly proportional to the potential difference (V)  across the conductor provided all physical conditions and temperature remains constant i.e.  I\propto V 	herefore\ \ V = IR Where  R  is the resistance of the conductor. 	extbf{Alternative form of Ohm's Law: } It states that, the current density (J)  through a conductor is proportional to the Electric Field (E)  across it. J = \sigma E Where  \sigma  is the conductivity of the conductor.

Question 8

Which is the S.I. unit of resistance ?

Accepted Answer

The electrical resistance of an electrical conductor is the opposition to the passage of an electric current through that conductor. The S.I. unit of electrical resistance is the ohm ( \Omega  ).The resistance  (R)  of an object is defined as the ratio of voltage across it  (V)  to current through it  (I) . That is,  R=\dfrac { V }{ I }  ohms.

Question 9

On what factors does the resistance of a conductor depends ? Write SI unit of resistance

Accepted Answer

The resistance of a conductor depends upon the resistivity, length and cross-sectional area of the conductor which is given by the relation  \left(R=\displaystyle\rho \dfrac{l}{A}\right) . It does also depend on other physical factors like temperature etc. Its SI unit is Ohm  (\Omega) .

Question 10

State Ohm's law. Draw a graph between voltage and current for a metallic conductor. Draw a circuit diagram of a circuit which consists of battery, ammeter, voltmeter, resistor, rheostat and a key.

Accepted Answer

The potential difference V across the ends of a given metallic wire in an electric circuit is directly proportional to the current flowing through it, its temperature should remain constant. This is called Ohm's law.

Revise with Concepts

Ohm's Law, Resistance and Resistivity

Dependence of Resistance on Shape, Size,Resistivity and Temperature

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Quick Summary With Stories

Ohm's Law

Ohm's Law, Resistance and Resistivity

Dependence of Resistance on Shape, Size and Resistivity

Resistance and Resistivity

Resistivity and Conductivity

Effect of Temperature on Resistance

Important Questions

A wire of length L and resistance R is stretched so that the length is doubled and area of cross section halved. How will (i) resistance change and (ii) resistivity change.

Two wires of same material have lengths $L$ and $2 L$ cross-sectional areas $4 A$ and $A$ respectively. The ratio of their resistances would be

(a) State Ohm's law.
(b) Describe an experiment to verify this law.

State and explain Ohm's law.

The voltage - current $(V - I)$ graph of a metallic conductor at two different temperature $T_{1}$ and $T_{2}$ is shown below. At which temperature is the resistance higher?

What length of copper wire of resistivity $1.7 \times 1 0^{- 8} Ω m$ and radius 1 mm is required so that its resistance is $1 Ω$ ?

State Ohms law?

Which is the S.I. unit of resistance ?

On what factors does the resistance of a conductor depends ? Write SI unit of resistance

State Ohm's law. Draw a graph between voltage and current for a metallic conductor. Draw a circuit diagram of a circuit which consists of battery, ammeter, voltmeter, resistor, rheostat and a key.

Revise with Concepts

Ohm's Law, Resistance and Resistivity

Dependence of Resistance on Shape, Size,Resistivity and Temperature

Learn with Videos

Quick Summary With Stories

Ohm's Law

Ohm's Law, Resistance and Resistivity

Dependence of Resistance on Shape, Size and Resistivity

Resistance and Resistivity

Resistivity and Conductivity

Effect of Temperature on Resistance

Important Questions

A wire of length L and resistance R is stretched so that the length is doubled and area of cross section halved. How will (i) resistance change and (ii) resistivity change.

Two wires of same material have lengths L and 2L cross-sectional areas 4A and A respectively. The ratio of their resistances would be

(a) State Ohm's law.(b) Describe an experiment to verify this law.

State and explain Ohm's law.

The voltage - current (V−I) graph of a metallic conductor at two different temperature T1​ and T2​ is shown below. At which temperature is the resistance higher?

What length of copper wire of resistivity 1.7×10−8Ωm and radius 1 mm is required so that its resistance is 1Ω?

State Ohms law?

Which is the S.I. unit of resistance ?

On what factors does the resistance of a conductor depends ? Write SI unit of resistance

State Ohm's law. Draw a graph between voltage and current for a metallic conductor. Draw a circuit diagram of a circuit which consists of battery, ammeter, voltmeter, resistor, rheostat and a key.

Two wires of same material have lengths $L$ and $2 L$ cross-sectional areas $4 A$ and $A$ respectively. The ratio of their resistances would be

(a) State Ohm's law.
(b) Describe an experiment to verify this law.

The voltage - current $(V - I)$ graph of a metallic conductor at two different temperature $T_{1}$ and $T_{2}$ is shown below. At which temperature is the resistance higher?

What length of copper wire of resistivity $1.7 \times 1 0^{- 8} Ω m$ and radius 1 mm is required so that its resistance is $1 Ω$ ?