Current, Resistance and Electricity MCQ Quiz - Objective Question with Answer for Current, Resistance and Electricity - Download Free PDF

Key Points

• The resistance (R) of a wire is given by the formula R = ρ(L/A), where ρ is the resistivity, L is the length, and A is the cross-sectional area.
• Since both wires have the same length and resistance, we can set up a ratio for their resistivities based on their cross-sectional areas.
• The ratio of their cross-sectional areas is 1 : 8, implying one wire has a cross-sectional area 8 times larger than the other.
• Given that resistance is inversely proportional to the area (A), the wire with the larger area will have a lower resistivity if all other factors are constant. However, since their resistances are the same and lengths are equal, the only way to balance the equation is if their resistivities are directly proportional to their areas, resulting in the ratio of resistivities being  ρ = R(A/L)
• \(\rho \propto \text{Area} \\ A_1:A_2=1:8 \\ \implies \rho_1:\rho_2=1:8 \ \ \)

Additional Information

Resistivity is a fundamental property of materials that quantifies how strongly a material opposes the flow of electric current. A low resistivity indicates a material that readily allows the flow of electric current. Resistivity is specific to each material and influences how it is used in electrical and electronic applications. For example:

• Copper has a low resistivity, making it an excellent choice for electrical wiring.
• Rubber, on the other hand, has a high resistivity, which makes it an effective insulator.
• The resistivity of materials can be affected by temperature; in most metals, resistivity increases with temperature.
• Semiconductors have resistivities that fall between those of conductors and insulators, which can be altered by doping with impurities and changes in temperature.

Key Points

• The potential at point A is given as 20 V, and there is no potential drop across the circuit element between A and B.
• Point B is connected directly to point A, without any resistive or reactive element causing a voltage change.
• The circuit diagram shows no components like resistors, capacitors, or batteries between points A and B.
• Thus, the potential at point B is the same as at point A, which is 20 V.

Correct option is: (2) 2.0 A

R_AB = (1Ω / 3Ω) in series with (2Ω / 4Ω)

⇒ (1 × 3) / (1 + 3) + (2 × 4) / (2 + 4)

= 3 / 4 + 8 / 6 = (9 + 16) / 12 = 25 / 12 Ω

Now total current through the cell

I = 50 / (25 / 12) = 24 A

I_1Ω = (3 / 4) × 24 = 18 A, I_3Ω = (1 / 4) × 24 = 6 A

I_2Ω = (4 / 6) × 24 = 16 A, I_4Ω = (2 / 6) × 24 = 8 A

Using junction rule at C,

I_CD = 18 − 16 = 2 A (from C to D)

Correct option is: (3) R / 16

After being cut into 8 equal pieces,

⇒ Resistance of each piece = R′ = R / 8

Each set has 4 pieces in parallel combination

1 / R'' = 8 / R + 8 / R + 8 / R + 8 / R 

⇒ Resistance of each set = R″ = R / 32

Both sets are connected in series

∴ R_eq = R″ + R″ = 2 × (R / 32) = R / 16

Calculation:

The loop ABCDEF will be similar to balance wheatstone bridge as 

5/3 = 2.5/1.5

Thus the circuit will be:

Thus the equivalent circuit will be 

The total resistance is R = 8/3 +1/3 +1.5 + 5.5 = 10 Ω  

The total current will be 

I = V/ R = 5 / 10 = 1/2 A.

CONCEPT:

• Electric Power: The rate at which electrical energy is dissipated into other forms of energy is called electrical power i.e.,

\(P = \frac{W}{t} = VI = {I^2}R = \frac{{{V^2}}}{R}\)

Where V = Potential difference, R = Resistance and I = current.

CALCULATION:

Given - Potential difference (V) = 220 V, power of the bulb (P) = 100 W and actual voltage (V') = 110 V

• The resistance of the bulb can be calculated as,

​\(\Rightarrow R=\frac{V^2}{P}=\frac{(220)^2}{100}=484 \,\Omega\)

• The power consumed by the bulb.

\(\Rightarrow P=\frac{V^2}{R}=\frac{(110)^2}{484}=25 \,W\)

CONCEPT:

Galvanometer:

• A galvanometer is used for detecting current in an electric circuit.
• The galvanometer is the device used for detecting the presence of small currents and voltage or for measuring their magnitude.
• The galvanometer is mainly used in the bridges and potentiometer where they indicate the null deflection or zero current.
• The potentiometer is based on the premise that the current sustaining coil is kept between the magnetic field experiences a torque.

EXPLANATION:

• From the above, it is clear that the galvanometer is the instrument used for detecting the presence of electric current in a circuit. Therefore option 1^st is correct.

​Additional Information 

Difference between Ammeter and Galvanometer:

• The ammeter shows only the magnitude of the current.
• The galvanometer shows both the direction and magnitude of the current.

Explanation:

Ammeter:

•  It is a device used to measure the current in a circuit.
• It is generally connected in series in a circuit. 
• This is because the current remains the same when devices are connected in series. 
• The ideal ammeter has low resistance because the reading will change as an extra resistance is added in series. 

Additional Information

Voltmeter:  

• It is a device used for measuring the electric potential difference between two points in an electric circuit.
• It is connected in parallel across the two points to measure the voltage drop between the points.
• This is because the potential difference remains the same if devices are connected in parallel. 
• The voltmeter has high resistance because the overall resistance will not change if low resistance path is offered to the current in form of voltmeter. 

CONCEPT:

• Heating effect of electric current: When a current is flowing in a circuit having resistance there is a heat dissipation due to the resistance. This is called the heating effect of electric current.
• The heat dissipated is given by:

Heat (H) = I² R t

Where I = the current flowing in the circuit, R = the resistance of the circuit, and t = the time taken

EXPLANATION:

Given that: current (I) = 2 A

Resistance = R

Heat dissipated = work done by the heater (H) = 200 J

Time (t) = 2 sec

Heat (H) = I² R t = 2² × R × 2 = 200 J

8 R = 200

Resistance of the heater (R) = 200/8 = 25 Ω 

Mistake Points

• SI unit of conductance is ohm-1 (mho) or ohm per meter or seimens.
• Here given ohm meter which is wrong

CONCEPT:

• Electrical conductance (K): 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 (K) = 1/R 

• Electrical resistance (R): The electrical resistance of a material refers to its opposition to the flow of current.
  • Its SI unit is Ohm (Ω). 

EXPLANATION:

The SI unit of conductance = 1/ (The SI unit of resistance) = 1/Ω = Ω^-1 = Siemens. Hence option 2 is correct.

• Ohm is the SI unit of resistance.
• Ampere is the SI unit of current.
• Ohm-meter is the SI unit of electrical resistivity which is the measure of an object's ability to oppose the flow of current.

CONCEPT:

• Electric charge: It is an intrinsic property of the elementary particles of matter which gives rise to electric force between various objects.

It is a scalar quantity.

• SI unit of electric charge is coulomb (C).
• The total charge on the conductor is given by q = It, when current flows through the conductor for some time.

Where I = current and t = time

CALCULATION:

Given - I = 5 A and t = 2 min = 120 s

• The total charge on the conductor is given by q = It

⇒ Q = It

⇒ Q = 5 × 120 = 600 C

CONCEPT:

• Electrical Conductivity: It is a property of a material that shows the ability of a material to carry current.
  • It is the opposite of electrical resistivity.
• The below table shows the electrical conductivity of different materials:

EXPLANATION:

• From the given options, Silver has the highest electrical conductivity, and Aluminum has the least.
• On a scale of 0 to 100 for electrical conductivity, silver ranks 100, with copper at 97 and gold at 76, aluminum at 60.
• Hence the correct answer is option 4.

CONCEPT:

• Resistivity (ρ): The property of a conductor that opposes the flow of electric current through them and independent of the shape and size of the materials but depends on the nature and temperature of the materials is called resistivity.
  • The unit for resistivity is the ohm-meter (Ω-m).
  • The resistivity of a material depends on its nature and the temperature of the conductor.
  • The resistivity of a material doesn't depend on its shape and size (length and area).
  • Materials that conduct electrical current easily are called conductors and have a low resistivity.
  • Materials that do not conduct electricity easily are called insulators and these materials have a high resistivity.
  • Resistivity is inversely proportional to the number of free electrons per unit volume of the conductor and to the average relaxation time of the free electrons in the conductor.
• Resistance: The property of any conductor that opposes 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:

R = ρL/A

where ρ is resistivity, L is the length and A is the area of the cross-section. 

EXPLANATION:

From the above discussion, we can say that

1. The resistivity doesn't depend on the dimensions (length, diameter, and area) of the conductor. 
2. The resistivity depends on the material of the conductor. So option 4 is correct.
3. The resistivity depends on the temperature of the conductor. But the effect of temperature is negligible.
4. The resistivity does not depend on the density of the conductor.

EXTRA POINTS:

Difference between resistivity and resistance:

CONCEPT:

• Resistance is the ability of any electrical component to resist electric current across it.
• Equivalent Resistance can be defined as the resistance of the resistor which will replace all the resistors between two points and will draw the same current between these two points as it was flowing Earlier.
• Ohms Law: At constant temperature, a potential difference is the product of current and resistance.

Series and Parallel Connection:

CALCULATION:

In the given diagram, the three 3Ω resistors are in parallel with each other.

The Equivalent resistance across them R' can be represented as 

\(\frac {1}{R'} = \frac{1}{3 Ω} + \frac{1}{3 Ω} + \frac{1}{3 Ω} \)

\(\implies \frac {1}{R'} = \frac{3}{3 Ω}\)

\(\implies R' = \frac{3 Ω }{3}\)

⇒ R' = 1Ω 

Now, this combination is in series with a 4Ω resistor.

So, Equivalent resistance

R = R' + 4Ω = 1Ω + 4Ω = 5Ω

So, 5Ω is the correct option.

CONCEPT: 

• Electric current: The rate of flow of charge is called electric current. It is denoted by I.

Electric current (I) = Electric charge (Q)/Time (t)

EXPLANATION:
Electric current is traditionally defined as the flow of positive charges.

• This is a convention that dates back to Benjamin Franklin, who initially defined the direction of electric current as the flow from positive to negative.
• So, based on the traditional definition, the correct answer is Positive charges
• However, it's important to understand that in many practical circumstances (such as in metal wires, which are a common context for discussing electric current), the actual mobile charge carriers are negatively charged electrons.
• The electrons move in the opposite direction to the defined direction of the current because of their negative charge.
• But despite this, we still stick to the conventional definition of current as the flow of positive charges.