Electricity Worksheet-13

Electricity Worksheet-13

1. Let the resistance of an electrical component remain constant while the potential difference across the two ends of the component decreases to half its former value. What change will occur in the current through it ?

2. Why are coils of electric toasters and electric irons made of an alloy rather than a pure metal ?

3. Draw a schematic diagram of a circuit consisting of a battery of three cells of 2 V each, a 5 ohm resistor, an 8 ohm resistor, and a 12 ohm resistor, and a plug key, all connected in series.

4. Draw a schematic diagram of a circuit consisting of a battery of three cells of 2 V each, a 5 ohm resistor, an 8 ohm resistor, and a 12 ohm resistor, and a plug key, all connected in series

Redraw the circuit putting in an ammeter to measure the current through the resistors and a voltmeter to measure the across the 12 ohm resistor. What would be the readings in the ammeter and the voltmeter ?

5. Judge the equivalent resistance when the following are connected in parallel.

(a) 1 Ω and 10⁶ Ω

(b) 1 Ω and 10⁸ Ω and 10⁶ Ω

6. An electric lamp of 100 Ω, a toaster of resistance 50 Ω and a water filter of resistance 500 Ω are connected in parallel to a 220 V source. What is the resistance of an electric iron connected to the same source that takes as much current as all three appliances and what is the current through it ?

7. What are the advantages of connecting electrical devices in parallel with the battery instead of connecting them in series.

8. How can three resistors of resistances 2 Ω, 3 Ω, and 6 Ω, be connected to give a total resistance of (a) 4 Ω (b) 1 Ω?

9. What is the highest and the lowest total resistance that can be secured by combinations of four coils of resistances 4 Ω, 8 Ω, 12 Ω, 24 Ω ?

10. Why does the cord of an electric heater not glow while the heating element does ?

Answer:

1. When the potential difference becomes half, the current through it also becomes half. Since I = V/R, when potential difference becomes V/2, current becomes I/2 as the resistance (R) of the component remains constant.

2. Coils of electric toasters and electric irons are made of nichrome which is an alloy (Ni: 60%, Cr : 12%, Mn : 2%, Fe : 26%).

This is due to the following reasons :

(i) resistivity of an alloy  is generally higher than that of its constituent metals (i.e., Ni, Cr, Mn and Fe)

(ii) it has a high melting point.

(iii) it does not oxidise (i.e., burn) when it is red hot (at 800°C).

4. The circuit diagram of with an ammeter A and a voltmeter V across the 12 Ω  resistor is shown in

Since all the three resistances are in series.

total resistance in the circuit, R = 5 Ω + 8 Ω + 12 Ω = 25 Ω

current in the circuit,           

Potential difference across 12 ohm resistor, i.e., V = current × resistance = 0.24 × 12 = 2.88 V

5. (a) Slightly less than 1 Ω. In parallel combination of resistors, the equivalent resistance is lesser than the least resistance (in this case, 1 Ω).

(b) Slightly less than 1 Ω.

6. Resistance of the electric lamp, r₁ = 100 Ω

resistance of toaster, r₂ = 50 Ω

resistance of water filter, r₃ = 500 Ω

Since r₁, r₂ and r₃ are connected in parallel, their equivalent resistance (R_P) is given by

or     

Current through the three appliances, i.e.,

since the electric iron connected to the same source (i.e., 220 V), takes as much current as all three appliance,     i.e., I, its resistance is equal to

R_P, I,e., 125/4 Ω  = 31.25 Ω

Current through the electric iron, I = 7.04 A

7. (a)    When a number of electrical devices are connected in parallel, each device gets the same potential difference as provided by the battery and a device keeps on working even if other devices fail. But in case of the devices are connected in series when one device fails, the circuit is broken and all other devices also stop working.

(b)    Parallel circuit is useful when each device has different resistance and each device requires different current for its operation as in this case the current divides itself through different devices. In series circuit same current flows through all the devices, irrespective of their resistances.

8. (a)    To get a total resistance of 4 Ω from resistors of resistances 2 Ω, 3 Ω, and 6 Ω; the resistors of resistances 3 Ω and 6 Ω should be connected in parallel. Their equivalent resistance is

This combination of equivalent resistance 2 Ω if connected in series with the resistor of resistance 2 Ω then the equivalent resistance of three resistors becomes 2 Ω + 2 Ω  = 4 Ω as shown in

(b)    To get a resistance of 1 Ω from three given resistors of resistances 2 Ω, 3 Ω, 6 Ω these should be connected in parallel. The equivalent resistance is given by

9. The highest resistance is secured when all the four coils are connected in series. In that case,

          R_s = 4 Ω + 8 Ω + 12 Ω + 24 Ω = 48 Ω

The lowest resistance is secured when all the four coils are connected in parallel.

10. The cord of an electric heater is made up of thick copper wire and it has much lower resistance than its element. For the same current flowing through the cord and the element, heat produced in the element is much more than that is produced in the cord. So the element becomes very hot and glows whereas the cord does hot become hot and does not glow.