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An engineering company is hired to improve the efficiency of a transmission line. In their report, they discuss ways that will allow them to reduce the current by a factor of four. Assuming this is done, by what factor will the power losses be reduced?

5 years ago

Answered By Leonardo F

The key concept here is how the power dissipation (P), electric current (i) and resistance (R) are related. The formula is:

 $P=\frac{V^2}{R}$P=V2R  

In which V is the potential difference of the circuit. According to first Ohm's law:

 $V=R\times i$V=R×i 

We will have:

 $P=\frac{\left(R\times i\right)^2}{R}$P=(R×i)2R  

 $P=R\times i^2$P=R×i2 

Basically, the power dissipation is the product between the electric resistance and the square of the electric current. Since the engineering company said that the electric current can be reduced by a factor of 4, the power losses (or dissipation) will be reduced by a factor of  $4^2$42 , or 16, if the total electric resistance of the circuit is constant.

Hence, the answer is 16.