Chapter 11: Electricity

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.

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.

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.

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.

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

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.

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.

The value of the resistor can be calculated using Ohm’s Law as follows:

In series connection, there is no division of current. The current flowing across all the resistors is the same.

To calculate the amount of current flowing across the resistors, we use Ohm’s law.

But first, let us find out the equivalent resistance as follows:

R = 0.2 Ω + 0.3 Ω + 0.4 Ω + 0.5 Ω + 12 Ω = 13.4 Ω

Now, using Ohm’s law,

The current flowing across the 12 Ω is 0.671 A.

Let us consider the number of resistors required as ‘x.’

The equivalent resistance of the parallel combination of resistor R is given by

The number of resistors required is 4.