Science
(a) State the law and write the formula connecting the electric current flowing through a conductor and voltage applied across it.
(b) In a household five fans each of 100 W are used for 4 hours and an electric press of 500 W for 2 hours every day. Calculate the cost of using the fans and electric press for 60 days if the cost of 1 unit of electrical energy is Rs. 6.5
Current Electricity
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Answer
(a) The relationship between the electric current flowing through a conductor and the voltage applied across it is given by Ohm’s Law.
Ohm’s Law : At constant temperature, the current (I) flowing through a conductor is directly proportional to the potential difference (V) applied across its ends, provided the physical conditions of the conductor remain constant.
Mathematically,
V ∝ I
or
V = IR
where:
- V = Potential difference (in volts, V)
- I = Current (in amperes, A)
- R = Resistance of the conductor (in ohms, Ω)
(b) Given,
- Number of fans (n) = 5
- Power rating of each fan (P1) = 100 W
- Daily usage time for fan (t1) = 4 hours
- Power rating of electric press (P2) = 500 W
- Daily usage time for the press (t2) = 2 hours
- Total number of days = 60
- Cost of 1 unit of electricity = Rs. 6.5
Total power consumed by the fans = n x P1 = 5 x 100 = 500 W
Total electrical energy consumed by the fans each day = Total power consumed by the fans x t1 = 500 x 4 = 2000 Wh
Similarly,
Total electrical energy consumed by the electric press each day = P2 x t2 = 500 x 2 = 1000 Wh
Now,
Total energy consumed by the fans and the press per day = 2000 + 1000 = 3000 Wh = 3 KWh
Then,
Total energy consumed by the fans and the press for 60 days = 3 x 60 = 180 KWh
As,
1 KWh = 1 unit
Then,
Total cost after 60 days = Total energy consumed by the fans and the press for 60 days x Cost of 1 unit of electricity
= 180 x 6.5
= ₹ 1170
Hence, the cost of using the fans and electric press for 60 days is ₹ 1170.
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