Answer - 22 : - Electric power is the rate of consumption of electrical energy by electric appliances. Hence, the rate at which energy is delivered by a current is the power of the appliance.

Question - 23 : - An electric motor takes 5 A from a 220 V line. Determine the power of the motor and the energy consumed in 2 h.

Answer - 23 : -

The power of the motor can be calculated by the equation,

P = VI

Substituting the values in the above equation, we get

P = 220 V × 5 A = 1100 W

The energy consumed by the motor can be calculated using the equation,

E = P × T

Substituting the values in the above equation, we get

P = 1100 W × 7200 = 7.92 × 10⁶ J

The power of the motor is 1100 W and the energy consumed by the motor in 2 hours is 7.92 × 10⁶ J.

Question - 24 : - A piece of wire of resistance R is cut into five equal parts. These parts are then connected in parallel. If the equivalent resistance of this combination is R′, then the ratio R/R′ is _____.

Answer - 24 : -

(a) 1/25 (b) 1/5

(c) 5 (d) 25

Answer:

d) 25

Explanation:

The resistance is cut into five equal parts, which means that the resistance of each part is R/5.

We know that each part is connected to each other in parallel, hence the equivalent resistance can be calculated as follows:

The ratio of R/R′ is 25.

Question - 25 : - Which of the following does not represent electrical power in a circuit?

Answer - 25 : -

(a) I²R

(b) IR²

(d) V²/R

Solution:

Answer: b) IR²

Explanation:

Electrical power is given by the expression P = VI. (1)

According to Ohm’s law,

V = IR

Substituting the value of V in (1), we get

P = (IR) × I

P = I²R

Similarly, from Ohm’s law,

I = V/R

Substituting the value of I in (1), we get

P = V × V/R = V²/R

From this, it is clear that the equation IR2 does not represent electrical power in a circuit.

Question - 26 : - An electric bulb is rated 220 V and 100 W. When it is operated on 110 V, the power consumed will be _____.

Answer - 26 : -

(a) 100 W (b) 75 W

Answer

25 W

Explanation:

The energy consumed by the appliance is given by the expression

P = VI = V²/R

The resistance of the light bulb can be calculated as follows:

R = V²/P

Substituting the values, we get

R = (220)²/100 = 484 Ω

Even if the supply voltage is reduced, the resistance remains the same. Hence, the power consumed can be calculated as follows:

P = V²/R

Substituting the value, we get

P = (110)² V/484 Ω = 25 W

Therefore, the power consumed when the electric bulb operates at 110 V is 25 W.

Question - 27 : - Two conducting wires of the same material and of equal lengths and equal diameters are first connected in series and then parallel in a circuit across the same potential difference.

Answer - 27 : -

The ratio of heat produced in series and parallel combinations would be _____.

(a) 1:2

(b) 2:1

(d) 4:1

Solution:

Let R_s and R_p be the equivalent resistance of the wires when connected in series and parallel respectively.

For the same potential difference V, the ratio of the heat produced in the circuit is given by

Hence, the ratio of the heat produced is 1:4.

Question - 28 : - How is a voltmeter connected in the circuit to measure the potential difference between two points?

Answer - 28 : - To measure the voltage between any two points, the voltmeter should be connected in parallel between the two points.

Question - 29 : - A copper wire has diameter 0.5 mm and resistivity of 1.6 × 10–8 Ω m. What will be the length of this

Answer - 29 : - wire to make its resistance 10 Ω? How much does the resistance change if the diameter is doubled?

Answer

The resistance of the copper wire of length in meters and area of cross-section m2 is given by the formula

The length of the wire is 122.72 m and the new resistance is 2.5 Ω.

Question - 30 : - The values of current I flowing in a given resistor for the corresponding values of potential difference V across the resistor are given below –

Answer - 30 : -

I (Ampere)	0.5	1.0	2.0	3.0	4.0
V (Volts)	1.6	3.4	6.7	10.2	13.2

Plot a graph between V and I and calculate the resistance of that resistor.

Answer

The plot between voltage and current is known as IV characteristic. The current is plotted in the y-axis while the voltage is plotted in the x-axis. The different values of current for different values of voltage are given in the table. The I V characteristics for the given resistor is shown below.

The slope of the line gives the value of resistance.

The slope can be calculated as follows:

Slope = 1/R = BC/AC = 2/6.8

To calculate R,

R = 6.8/2 = 3.4 Ω

The resistance of the resistor is 3.4 Ω.

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Chapter 12 – Electricity Solutions

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