Resistance Formula Important Questions

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Very Short Answer Questions (1 mark)

Ques. Plot the graph between current and voltage for GaAs. [Delhi 2014]

Ans. The Current Vs Voltage for GaAs is as Follows:

V-I plot for GaAs

Ques. How does resistivity of Cu vary as a function of temperature? [Delhi 2014, All India 2014]

Ans. The resistivity of Cu varies as per the following plot with respect to temperature.

The resistivity of Cu Vs Temperature

Read More: Static Electricity

Ques. Plot the resistivity of Silicon with temperature. [Delhi 2014]

Ans. The plot of resistivity of Cu as a function of temperature is:

Si Resistivity Vs Temperature

Ques. Define resistivity and give its Si unit. [All India 2011]

Ans. The resistance offered by unit length of the conductor across an area of 1 m² is termed as resistivity. The unit is Ohm- meter, denoted by Ωm.

Ques. Give the expression for the resitivity of a conductor with variation shown along a range of temperatures. [Delhi 2008]

Ans. The resistivity for a metallic conductor varying across a range of temperatures is given by the expression:

\(\rho_T=\rho_0[1+\alpha[T-T_0]]\)

Where

T, T₀= Temperatures

ρ_T, ρ₀ = Resistivities at temperatures T and T₀

α= Temperature Coefficient of the metallic conductor material

Read More:

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Short Answer Questions (2 Marks)

Ques. Differentiate between resistivity and resistance for a conductor. 

Ans. Resistance is the potential drop across the conductor per unit of current flowing through it. Resistivity is the resistance offered by a conductor unit cross-sectional area and unit length of the conductor. 

Ques. Show the variation of resistivity for a conductor and semiconductor concerning temperature change.

Ans. The following is the resistivity vs temperature plot of conductor and semiconductor:

Conductor (left), Semiconductor (Right)- Resistivity vs Temperature Plot

In conductors when temperature is raised, the resistivity increases,as the relaxation time decreases. Whereas in semiconductors, with an increase in temperature,relaxation time is decreased thereby reducing resistivity. 

Ques. A carbon resistor consists of three red colored strips and one gold strip. Determine the resistor value and tolerance.

Ans. For the carbon resistor the color code would be R R R Gold. The resistor value would be 22 x10² Ω ∓ 5 %. i.e. 2200 Ω with  ∓ 5 % tolerance.

Read More: Galvanometer 

Ques. What are ohmic and non-ohmic resistors? Give examples. 

Ans. Materials that obey Ohm’s Law are Ohmic resistors. Examples: Metals

Materials that do not follow Ohm’s Law and have their characteristics are non-ohmic resistors. Example diodes, transistors.

Ques. Why are constantan and manganin used for making resistors?

Ans. High resistivities and low temperature of coefficient resistance are why constantan and manganin alloys are used in resistors. 

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Long Answer Questions (3 Marks)

Ques. Why is a potentiometer used to measure the emf in a circuit? 

Ans. Potentiometer works on the principle of null deflection. Therefore, a potentiometer does not draw any current from the circuit. The emf value of a cell is the terminal potential difference when no current flows through the cell. Thus a potentiometer is used in place of a voltmeter to measure the emf of a cell. 

Ques. If V is the potential difference applied across length L of a copper wire and has a diameter D. What is the drift velocity of electrons if:

1. V is doubled
2. I is doubled
3. D is doubled

Ans. Drift velocity is given by V_d. 

Mathematically,

\(V_d=\frac{V}{R(neA)}\)

Replacing R with \(P \frac{l}{A}\)

\(V_d=\frac{V}{nePl}\)

Thus when the drift velocity gets doubled with a doubled V. Drift velocity gets halved when I is doubled it remains unchanged with a change in diameter. 

Read More: Unit of Voltage MCQs

Ques. What happens to the wire resistance when its length is increased to twice its original length? 

Ans. \(R=\rho \frac {l}{A}\)

⇒ \(R=\rho \frac {l}{\pi r^2}\)

When the length l₁= 2l the radius changes from r to r₁.

⇒ πr²l = πr₁²l₁

⇒ r₁²= r²/2

Substituting for new resistance we get

\(R'=\rho \frac {l_1}{\pi r_1^2} \)

\(R'=\rho \frac {2l}{\pi \frac{r^2} {2}} \)

⇒ \(R'=\rho \frac {4l}{\pi r^2} \)

Hence the resistance increases by four times in doubling the length.

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Very Long Answer Questions (5 Marks)

Ques. What is the expression for current density of a conductor in terms of drift speed of electrons? 

Ans. Let V be the potential difference applied across the conductor and E be the electric field produced inside the conductor. 

The derivation for the current density is as follows:

Read More: SI unit of Electric Current

Ques. If three resistors are combined in parallel and value at 2, 4, and 5 Ω respectively. Determine the total resistance of the combination. When connected to a 20 V emf battery and there is negligible internal resistance in the circuit, calculate the current through each resistor and the total current drawn from the battery. 

Ans. Let R₁, R₂, and R₃ be the three resistors.

When connected in parallel, the total resistance = \(\frac{1}{R}= \frac{1}{R_1}+ \frac{1}{R_2}+\frac{1}{R_3}\)

= \(\frac{1}{2}+\frac{1}{4}+\frac{1}{5}\)

= 20/ 19 Ω

EMF, V =20 V

Current I₁ through R₁ is 20/2 =10 A

Current I₂ through R₂= 20/4 =5A

Current I₃ through R₃= 20/5 =4A

Therefore, Total current = I₁+I₂+I₃

= 10+5+4=19 A

Discover about the Chapter video:

Current Electricity Detailed Video Explanation:

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