Question

An electrical cable having a resistance of $0.2 \,\Omega$ delivers $10\,kw$ at $200\,V\, D.C$. to a factory. What is the efficiency of transmission?

• A. $65\%$
• B. $75\%$
• C. $85\%$
• D. $95\%$

Answer 1

Answer: (D)

$95\%$

Answer 2

Power $P=VI$
$\Rightarrow I=\frac{P}{V} =\frac{10\times10^{3}}{200}$
$=50\,A$
$\therefore$ Power loss $=I^{2}R= (50)^{2} \times(0.2)$
$=500 \,W$
Therefore, efficiency of transmission
$=\frac{10000 \times100}{10000+500}$
$=95.23\%$
$=95\%$ (approx.)

The formula for electrical power has been derived from Ohm’s Law. It connects time, voltage, and charge. The formula for electric power is:

P = IV

By Ohm’s Law, it can also be written as:

P = I2R

Or

P = V2/R

Where,

P = Electric Power

I = Electric current

R = Resistance

V = Voltage or Potential difference

Power is the pace at which energy is used. Depending on whatever way the power integral is pointing, the electric circuit element alternates between being positive and negative repeatedly over a period of time. Power consumption may be stated as follows if the power remains constant across the time period:

E = Pt

P = E/t

Where,

• E = Energy Produced
• P = Power Consumption
• T = Time period