Two metallic wires A and B of the same length are made of the same material. The radius of wire A is double the radius of wire B. What is the ratio of resistances of the two wires? [3]
OR
There are three 220V-60W electric lamps and two 220V-100W electric fans in the house. The electric lamps are lit for 5 hours a day and the fans are run for 10 hours a day. If the cost per B.O.T unit is Rupees 5, what will be the cost of electricity for 30 days? [3]
R = ρ {l}\over {a}
or,R = ρ {l}\over πr^2
⇒ R ∝ 1\over r^2
⇒ {R_A} \over {R_B} = {{r_B}^2\over {r_A}^2
Given: rA = 2rB
⇒ R_A\over R_B = {{r_B}^2\over {2r_B}^2
⇒ R_A\over R_B = {{r_B}^2\over 4{r_B}^2
⇒ R_A\over R_B = 1\over 4
∴ The ratio of resistances of the two wires 1 : 4.
OR
Energy Consumption of the Lamps
- Power of each lamp = 60 W
- Total power for 3 lamps = 3 × 60 W = 180 W
- Daily energy consumption = 180 × 5 hours = 900Wh
Energy Consumption of the Fans
- Power of each fan = 100 W
- Total power for 2 fans = 2 × 100 W = 200 W
- Daily energy consumption = 200 W × 10 hours = 2000 Wh
Total Energy Consumption per Day
= 900Wh + 2000 Wh
= 2900 Wh
= 2.9 kWh
Total Energy Consumption (30 Day) = 2.9 kWh × 30
= 87 kWh
Total cost = ₹ 5 × 87 = ₹ 435
Related Questions
More WBBSE Hard level questions