Final answer:
The efficiency of a 30,000 W power transmission at 5000 V over 15 Ohms transmission lines is 98.2% after calculating power dissipation and subtracting it from the shipped power.
Step-by-step explanation:
To calculate the efficiency of power transmission, we need to consider the power delivered and the power lost in the transmission lines. Given a power shipment of 30,000 W (or 30 kW) at 5000 V over transmission lines with a resistance of 15 Ohms, we first determine the current using the formula P = IV, where P is power, I is current, and V is voltage. Solving for I, we get I = P / V = 30,000 W / 5000 V = 6 A.
Next, we find the power dissipated in the transmission lines using P = I²R, where P is power, I is current, and R is resistance. Plugging in the values, we get P = (6 A)² * 15 Ohms = 540 W.
The efficiency of the transmission can then be calculated by subtracting the power lost in the lines (540 W) from the power shipped (30,000 W) and then dividing by the power shipped, multiplied by 100 to get a percentage. Efficiency = ((30,000 W - 540 W) / 30,000 W) * 100 = 98.2%.
Therefore, the efficiency of the transmission is 98.2%.