A line having a total resistance of 0.20 Ωdelivers 10.00 kW at 250 V to a small factory. What i

step 1 high in this given problem total resistance of the line wire that is given as r is equal to 0 .2

A line having a total resistance of 0.20 Ωdelivers 10.00 kW...

A line having a total resistance of $0.20 \Omega$ delivers $10.00 \mathrm{~kW}$ at 250 $\mathrm{V}$ to a small factory. What is the efficiency of the transmission? The line dissipates power due to its resistance. Consequently we'll need to find the current in the line. Use $\mathrm{P}=V I$ to find $I=\mathrm{P} / \mathrm{V}$. Then $$ \begin{array}{l} \text { Power lost in line }=I^{2} R=\left(\frac{P}{V}\right)^{2} R=\left(\frac{10000 \mathrm{~W}}{250 \mathrm{~V}}\right)^{2}(0.20 \Omega)=0.32 \mathrm{~kW} \\ \text { Efficiency }=\frac{\text { Power delivereed by linc }}{\text { Power supplied to line }}=\frac{10.00 \mathrm{~kW}}{(10.00+0.32) \mathrm{kW}}=0.970=97.0 \% \end{array} $$

A line having a total resistance of $0.20 \Omega$ delivers $10.00 \mathrm{~kW}$ at 250 $\mathrm{V}$ to a small factory. What is the efficiency of the transmission?
The line dissipates power due to its resistance. Consequently we'll need to find the current in the line. Use $\mathrm{P}=V I$ to find $I=\mathrm{P} / \mathrm{V}$. Then
$$
\begin{array}{l}
\text { Power lost in line }=I^{2} R=\left(\frac{P}{V}\right)^{2} R=\left(\frac{10000 \mathrm{~W}}{250 \mathrm{~V}}\right)^{2}(0.20 \Omega)=0.32 \mathrm{~kW} \\
\text { Efficiency }=\frac{\text { Power delivereed by linc }}{\text { Power supplied to line }}=\frac{10.00 \mathrm{~kW}}{(10.00+0.32) \mathrm{kW}}=0.970=97.0 \%
\end{array}
$$

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Key Concepts

Transmission Efficiency

Transmission efficiency refers to the ratio of the useful power delivered to the load compared to the total power supplied, including losses in the transmission system. It is a key measure used to evaluate how effective a transmission line or network is in delivering power, with losses usually arising from the inherent resistance in conductors.

Resistive Power Loss (Joule Heating)

Resistive power loss is the energy dissipated as heat in a conductor due to its electrical resistance, a phenomenon described by Joule's law. This loss is calculated using the I²R formula, where the current squared multiplied by the resistance gives the power converted into heat, lowering the overall efficiency of the power delivery system.

Power-Voltage-Current Relationship

The relationship between power, voltage, and current is foundational in understanding electrical circuits, expressed by the formula P = IV. This equation allows one to determine one electrical quantity if the other two are known, and is crucial in calculating the current that flows through a system when the power delivered and voltage are specified.

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