VARDAAN LEARNING INSTITUTE

Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.

1. Assertion: The resistivity of a semi-conductor decreases with increase of temperature.
   Reason: At higher temperatures, more electrons are free to move in semiconductors.
2. Assertion: Fuse wire must have high resistance and low melting point.
   Reason: Fuse is used for small current flow only.
3. Assertion: When a wire is stretched to three times its length, its resistance becomes 9 times.
   Reason: Resistance is directly proportional to the square of length when volume is constant.
4. Assertion: Current is a scalar quantity.
   Reason: Electric current does not follow vector laws of addition.
5. Assertion: 40 W bulb glows brighter than 100 W bulb when connected in series.
   Reason: In series combination, power dissipated is $I^2R$ and resistance of 40 W bulb is greater.
6. Assertion: A bird perches on a high power line and nothing happens to the bird.
   Reason: The level of bird is very high from the ground.
7. Assertion: It is advantageous to connect electric appliances in parallel.
   Reason: In parallel, if one device fails, others continue to work.
8. Assertion: Bending a wire does not affect its electrical resistance.
   Reason: Resistance of a wire is proportional to resistivity of material.
9. Assertion: Alloys are commonly used in electrical heating devices.
   Reason: Alloys do not oxidize (burn) readily at high temperatures.
10. Assertion: Two unequal resistors are connected in series. The potential drop across the larger resistance is more.
    Reason: In series, $V=IR$ and $I$ is constant.

Case I: Residential Electricity. The values of current \( I \) flowing in a given resistor for the corresponding values of potential difference \( V \) across the resistor are given below.

11. Plot a graph between \( V \) and \( I \) and calculate the resistance of that resistor.
12. What is the nature of the graph obtained?
13. Is the resistor obeying Ohm's Law? Justify.
14. If the length of this wire is doubled, what will be the new resistance?

Case II: The Electric Bill. A household uses the following electric appliances:
(i) Refrigerator of rating 400 W for 10 hours each day.
(ii) Two electric fans of rating 80 W each for 12 hours each day.
(iii) Six electric tubes of rating 18 W each for 6 hours each day.
The electricity bill for the month of June is to be calculated.

15. Calculate the total energy consumed by the refrigerator in June (30 days).
16. Calculate the total energy consumed by fans and tubes in one day.
17. If the cost per unit is Rs 3.00, what is the total electricity bill for June?
18. How can the family reduce this bill? Suggest one scientific method.

19. A wire of resistance 20 $\Omega$ is bent in the form of a closed circle. What is the effective resistance between the two ends of any diameter?
20. Find the equivalent resistance between points A and B in an equilateral triangle circuit where each side has a resistance of 6 $\Omega$.
21. A 100 W bulb B1, and two 60 W bulbs B2 and B3, are connected to a 250 V source. ONE 60W bulb is in series with the 100W bulb, and the other 60W bulb is in parallel to this series combination. Find the current flowing through any one of the 60 W bulbs. (Assume R is constant).
22. Given $n$ resistors each of resistance $R$. How will you combine them to get the (i) maximum and (ii) minimum effective resistance? What is the ratio of the maximum to minimum resistance?
23. Compare the power used in the 2 $\Omega$ resistor in each of the following circuits: (i) a 6 V battery in series with 1 $\Omega$ and 2 $\Omega$ resistors, and (ii) a 4 V battery in parallel with 12 $\Omega$ and 2 $\Omega$ resistors.
24. Two lamps, one rated 100 W at 220 V, and the other 60 W at 220 V, are connected in parallel to electric mains supply. What current is drawn from the line if the supply voltage is 220 V?
25. Which uses more energy: a 250 W TV set in 1 hr, or a 1200 W toaster in 10 minutes?
26. An electric heater of resistance 8 $\Omega$ draws 15 A from the service mains 2 hours. Calculate the rate at which heat is developed in the heater.
27. What is the commercial unit of electrical energy? Represent it in terms of Joules.
28. 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. Find the ratio of heat produced in series and parallel.
29. Should the heating element of an electric iron be made of iron, silver or nichrome? Why?
30. Explain why a bird perched on a high voltage transmission line does not get electrocuted, but if it touches two lines simultaneously, it dies.
31. Derive the expression for the heat produced due to a current 'I' flowing for a time interval 't' through a resistor 'R' having a potential difference 'V' across its ends.
32. Why does the cord of an electric heater not glow while the heating element does?
33. A wire of resistivity $\rho$ is stretched to twice its length. What will be its new resistivity?