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CBSE Class 10 Science 2020 Outside Delhi Set 3

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Question : 6 of 6
Marks: +1, -0
(a) An electric bulb is rated at 200 V200 \text{ V}; 100 W100 \text{ W}. What is its resistance?
(b) Calculate the energy consumed by 3 such bulbs if they glow continuously for 10 hours for complete month of November.
(c) Calculate the total cost if the rate is 6.50 per unit.
OR
(a) What is meant by the statement, "The resistance of a conductor is one ohm" ?
(b) Define electric power. Write an expression relating electric power, potential difference and resistance.
(c) How many 132Ω132 \, \Omega resistors in parallel are required to carry 5 A5 \text{ A} on a 220 V220 \text{ V} line?
Solution:  
(a) Here, potential difference across the bulb, V=200 VV = 200 \text{ V}
Power of the bulb, P=100 WP = 100 \text{ W}
As P=V2R,R=V2P=(200 V)2100 WP = \frac{V^2}{R}, \quad R = \frac{V^2}{P} = \frac{(200 \text{ V})^2}{100 \text{ W}}
=4×104100Ω=400Ω= \frac{4 \times 10^4}{100} \, \Omega = 400 \, \Omega
(b) Electric energy consumed by 1 bulb in 10 hours for 30 days, i.e.,
W=PtW = P t
=100 W×10×30= 100 \text{ W} \times 10 \times 30
=30000 Wh= 30000 \text{ Wh}
Electric energy consumed by 3 bulbs
=30000×3= 30000 \times 3
=90000 Wh= 90000 \text{ Wh}
=90 kWh= 90 \text{ kWh}
=90 unit= 90 \text{ unit}
(c) Cost of 90 units of electric energy
=90×6.50=585 . = 90 \times 6.50 = \text{₹} 585 \text{ . }
OR
(a) Ohm's law states that current flowing through a conductor is directly proportional to the potential difference maintained across the two ends of a conductor at constant temperature and pressure.
Let current flowing through a conductor is I,VI, V is the potential difference maintained across the two ends of conductor.
As per Ohm's law, VIV \propto I
Thus,
V=IRV = I R
Here RR is a proportionality constant called resistance.
As per the question, the resistance of a conductor is 1 ohm1 \text{ ohm}.
Let V=1V=1 volt and I=1 AI=1 \text{ A}, then R=1 ohmR=1 \text{ ohm} Hence, the resistance is said to be 1 ohm1 \text{ ohm} if 1 ampere of current flows through a circuit due to the potential difference of 1 volt.
(b) Electric power is the rate at which work is done or energy is transformed in an electrical circuit.
The formula for electric power is given by:
P=VIP = V I
where,
PP is the power
VV is the potential difference in the circuit I is the electric current
Power can also be written as
P=I2RP = I^2 R
P=V2RP = \frac{V^2}{R}
The above two expressions are got by using Ohms law, where, voltage, current
and resistance are related by the following relation.
Where,
RR is the resistance in the circuit.
VV is the potential difference in the circuit I is the electric current
(c) For xx number of resistors of resistance 132Ω132 \, \Omega
Supply voltage, V=220 VV = 220 \text{ V}
Current, I=5 AI = 5 \text{ A}
Equivalent resistance of the combination =R=R, given as
1R=x×1132\frac{1}{R} = x \times \frac{1}{132}
R=132xR = \frac{132}{x}
From Ohm's law :
132x=2205132 x = \frac{220}{5}
132x=44132 x = 44
132=44x132 = 44 x
x=13244x = \frac{132}{44}
x=3x = 3
So, answer is 3 resistors.
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