1. 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 –
(a) 1/25 (b) 1/5 (c) 5 (d) 25
Answer: (d) 25
[ When a wire of resistance R is cut into five equal parts and these parts are connected in parallel,
Let R be the resistance of each of the five equal parts .
Since the five equal parts are cut from the original wire of resistance R, each part's resistance will be .
Therefore, the correct answer is (d) 25. ]
2. Which of the following terms does not represent electrical power in a circuit?
(a) (b) (c) (d)
Answer: (b)
3. An electric bulb is rated 220 V and 100 W. When it is operated on 110 V, the power consumed will be –
(a) 100 W (b) 75 W (c) 50 W (d) 25 W
Answer: (d) 25 W
[ The electric bulb is rated at 220 V and 100 W.
Let, R be the first resistance :
The power consumed (P') when the bulb is operated at 110 V:
So, the power consumed by the electric bulb when operated on 110 V is 25 W.
The correct answer is (d) 25 W ]
4. 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. The ratio of heat produced in series and parallel combinations would be –
(a) 1:2 (b) 2:1 (c) 1:4 (d) 4:1
Answer: (c) 1 : 4
[ Let R be the resistance of each conducting wire .
When the wires are connected in series, the total resistance
When the wires are connected in parallel, the total resistance ,
The formula for heat produced in a resistor is given by:
The ratio of heat produced in series to parallel combinations would be:
And
So, the ratio of heat produced in series to parallel combinations is 4 : 1.
The correct answer is (d) 1 : 4 ]