Resistance MCQ Quiz in मल्याळम - Objective Question with Answer for Resistance - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

The correct answer is 'option 2'

Solution:

The resistance of the wire is given by

\(R={\rho L\over A}\)

when the wire is stretched to increase its length by 1% the new length is

\(L'=L+\frac{1}{100}L=1.01L\)

The volume of wire remains the same hence

V=AL=A'L' 
where A' is the new area of cross-section of the wire.

\(A'=\frac{L}{L'}\implies A'=\frac{A}{1.01} \)

Now, the changed resistance is

\(R'={\rho L'\over A'}\)

\(R={\rho (1.01L)\over \frac{A}{1.01}}\)

\(R'={\rho L\over A}(1.01)(1.01)=R(1.02)\)

\(\implies\frac{R'}{R}=1.02\)

The percentage increase in resistance is

\((\frac{R'}{R}-1)\times 100=0.02\times 100=2\%\)

Calculation:

Rating of each lamp = 15 V, 10 W

Rated current of lamp = \(\frac{10}{15} = \frac{2}{3} \ A\)

As each element are connected in a series current will be \(\frac{2}{3}\)A in the circuits.

∴ The equivalent impedance of the circuit = V/I = 300 ÷ \(\frac{2}{3}\) 

\(= \frac{300 \times 3}{2} = 450 \ Ω \)

Resistance of each lamp = \(\frac{(15)^2}{10} = 22.5 \ Ω\)

∴ Total resistance = R + R_L1 + R_L2 = 450

⇒ R = 450 - 22.5 - 22.5

⇒ R = 405 Ω

Hence, correct option is (2)

Resistance:

It is the property of any conductor that opposes or impedes the flow of electric current through it and depends on the shape and size of the materials, temperature, and nature of the materials is called resistance.

It is denoted by R and the SI unit is the ohm (Ω).

The resistance is given by:

\(\Rightarrow R=\frac{\rho l}{A}\)

Where R = Resistance  

ρ = Resistivity 

l = Length of the wire (l = NL)

N = Number of turns

L = Mean length per turn

A = Cross-sectional area

Calculation:

V (Supply Voltage) = 110 V

ρ = 0.04 μΩ m

N = 4000

L = 60 cm = 60 × 10^-2 m / turn

A = 0.6 mm2 = 0.6 × 10-6 m²

l = NL = 4000 × 60 × 10-2 = 2400 m

Resistance \(\Rightarrow R=\frac{\rho l}{A} = \frac{0.04 \times 10^{-6} \times 2400}{0.6 \times 10^{-6}}=160\;\Omega \)

Power absorbed = V² / R = 110² / 160 = 75.625 W

Important Points

• Conductance is a property of a conductor that allows the flow of current through it.
• Reluctance is a property of a conductor that opposes the passage of magnetic flux lines through it
• Permeance is a property of a conductor that allows the passage of magnetic flux lines through it

Concept:

The formula for internal resistance 

\(r = \frac{{E - {V_T}}}{I}\)  ..(1)

Where E = open circuit voltage

V_T = terminal voltage 

I = supplying current

r = internal resistance

Calculation:

Given,

E = 2 V, V_T = 1 V, I = 5 A

From equation(1)

\(r = \frac{{2 - 1}}{5}\)

r = 0.2 Ω 

Rating of resistor:

Resistance is an element of a circuit or network which is inserted to lower the current in the circuit.

The unit of resistance is ohm and its symbol is Ω.

Usually, voltage V is constant 230 V (RMS) in household supply and wattage, P = V²/R

So, if we fix the value of R, Wattage(Power) will be fixed.

Or we can say if we know anyone between resistance(R) and wattage (P), others can be known.

Thus, the rating is ohmic and wattage for a resistor.

The correct answer is (option 1) i.e. \(\frac{\textbf{3}}{\textbf{8}}\: \Omega\)

Concept:

In a series connection,

Total resistance, R_T = R₁ + R₂ + R₃

And Total conductance, 

\(G_T=\frac{1}{R_T}=\frac{1}{R_1+R_2+R_3}\)

Also, \(\frac{1}{G_T}=\frac{1}{G_1}+\frac{1}{G_2}+\frac{1}{G_3}\)

Here, \(G_1=\frac{1}{R_1}\)

 \(G_2=\frac{1}{R_2}\)

 \(G_3=\frac{1}{R_3}\)

Calculation:

Given,

G₁ = 4 ℧, G₂ = 8 ℧

\(\frac{1}{G_T}=\frac{1}{G_1}+\frac{1}{G_2}\)

 \(\Rightarrow G_T= \frac{G_1G_2}{G_1+G_2} \)

\(=\frac{4\times 8}{4+8}=\frac{8}{3} \: \mho\)

∵ \(R_T=\frac{1}{G_T}\)

∴ \(R_T=\frac {3}{8}\: \Omega\)

Electrical conductance (G): The reciprocal of electrical resistance is called conductance.

 It is a measure of how easily current can flow through a material.

Its SI unit is Siemens (℧).

Electrical conductance (G) = 1/R = 1/Ω = mho

Electrical resistance (R): The electrical resistance of a material refers to its opposition to the flow of current.

Its SI unit is Ohm (Ω). 

Concept:

• Resistances are available in small as well as in large values.
• The resistors are generally painted by a specific colour and a specific code is assigned to them. This is called colour coding of the resistance.
• The resistance value, tolerance, and wattage rating are generally printed on the body of the resistor as numbers or letters.

Colour Coding of Resistance: To know the value of resistance colour code is used

1. Colour band A and B: Indicate the first two significant figures of resistance in ohms.
2. Band C: Indicates the decimal multiplier i.e. the number of zeros that follows the two significant figures.
3. Band D: Indicates the tolerance in percentage about the indicated value or in other words, it represents the percentage accuracy of the indicated value.
4. The tolerance in the case of gold is ±5% and in silver is ±10%. If only three bands are marked on carbon resistance, then it indicates a tolerance of 20%.

CALCULATION:

Option 1

R₁ = 24 × 10³ ± 5%

Option 2

R2 = 42 × 103 ± 5%

Option 3

R3 = 23 × 104 ± 5%

Option 4

R4 = 34 × 102 ± 5%

The least value of resistor is R₄ (option 4).

Important PointsThe table for the resistor colour code is given below:

​TRICK TO REMEMBER COLOUR CODE:

• BBROYGBVGW stands for “Black Brown Red Orange Yellow Green Blue Violet Gray White”, electronic colour codes of the resistor.

Alternate one:

Big Boys Race Our Young Girls But Violet Generally Wins

Given:

R₁ = 6 Ω

R₂ = 2 Ω

R₃ = 6 Ω

R₄ = 2 Ω

R₃₄ = R₃ + R₄  = 6 + 2 = 8 Ω

R’ = R₂ ll R₃₄ = (2×8)/(2+8) = 16/10 = 1.6 Ω

R_eq = R₁ + R’ = 6 + 1.6 = 7.6 Ω

The circuit after removing the voltage source

The total resistance of the new circuit will be the equivalent resistance of the network.

R_eq = R_t = 3 + 2 + 2 = 7 Ω 

The equivalent resistance of the network is 7 Ω.

 Mistake Points While finding the equivalent resistance of the network, don't consider the internal resistance of the voltage source.