. An electrical cable having a resistance of 0.2 Ω delivers 10 kW at 200 V DC to a factory. What is the efficiency of transmission?
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Current (I) = P / V = 10,000 / 200 = 50 A Show more…
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An electrical cable having a resistance of $0.2 \Omega$ delivers $10 \mathrm{~kW}$ at $200 \mathrm{~V} \mathrm{DC}$ to a factory. What is the efficiency of transmission? (a) $65 \%$ (b) $75 \%$ (c) $85 \%$ (d) $95 \%$
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 $I=\mathrm{P} / V$. Then Power lost in line $=I^{2} R=\left(\frac{\mathrm{P}}{V}\right)^{2} R=\left(\frac{10000 \mathrm{~W}}{250 \mathrm{~V}}\right)^{2}(0.20 \Omega)=0.32 \mathrm{~kW}$ $$ \text { Efficiency }=\frac{\text { Power delivered by line }}{\text { Power supplied to line }}=\frac{10.00 \mathrm{~kW}}{(10.00+0.32) \mathrm{kW}}=0.970=97.0 \% $$
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