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SSC JE Electrical 2019 with solution SET-1
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Three lamps are connected in series across a 120V supply and take a current of 1.5A. If the resistance of two of the lamps is 30Ω, what is the resistance of the third lamp?

Method 1

Supply Voltage = 120 V

Current I = 1.5 A

Total Resistance R = V/I = 120/1.5 = 80 Ω

Now resistance of 3 lamp be R1, R2, & R3

Req = R1 + R2 + R3

80 = 30 + 30 + R3

R3 = 20 Ω

Method 2

Applying KVL on the above circuit

120 = 1.5(R1 + R2) + 1.5R3

120 = 1.5(30 + 30) + 1.5R3

120 = 90 + 1.5R3

R3 = 30/1.5

R3 = 20 Ω

SSC JE Electrical 2019 with solution SET-1
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The law that explains about the economic size of a conductor is:

In transmission lines, a large amount of power is transmitted over a long distance. So, voltage regulation is not important because in some lines, 40% regulation is considered satisfactory. In such cases, only the economy is important. The cost of the conductor is the main part which decides the total cost of the transmission line. Hence, the selection of the proper size of the conductor for a particular line is most important.

The most economical area of the conductor is that for which the total annual cost of the transmission line is minimum. This is known as Kelvin’s law and was given by Lord Kelvin in the year 1881.

It states that the most economical cross-section of a conductor is the value at which the annual cost of the electric energy wasted in the conductor, and annual cost of the interest and depreciation on the capital cost of the conductor are equal. Thus, the total annual charge on an overhead transmission line can be expressed as :

Total annual charge =P1 + P2α or Variable part of the energy charge = Annual cost of energy wasted.

where

P1 and P2 are constants

α is the area of the X-section of the conductor.

SSC JE Electrical 2019 with solution SET-1
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The ratio of average energy demand to maximum demand during a specific period in

The ratio of average energy demand to maximum demand during a specific period is called the load factor.

Load Factor = Average Load/Maximum Demand