Physics 2000 JAMB Past Questions - Question 49: An electric generator with a power output of 3.0 kw at a voltage of 1.5kV distributes power along cables of total resistance 20.0Q. The power loss in the cable is

Correct Answer

D

Explanation

Power loss =I2R ;I=P/V =3000/1500 =2APower loss =2*2*20 =80ohmsTo find the power loss in the cables, you can use the formula for power loss in a resistor:

Power Loss (P_loss) = I^2 * RThe power loss in the cables can be calculated using the formula:

P_loss = I^2 * R

where P_loss is the power loss, I is the current flowing through the cables, and R is the resistance of the cables.

To find the current flowing through the cables, we can use Ohm's Law:

I = V / R_total

where V is the voltage and R_total is the total resistance of the cables.

In this case, the power output of the generator is given as 3.0 kW, which is equivalent to 3000 W, and the voltage is given as 1.5 kV, which is equivalent to 1500 V. The total resistance of the cables is given as 20.0 Ω.

First, let's calculate the current flowing through the cables:

I = 1500 V / 20.0 Ω
I = 75 A

Now, we can calculate the power loss in the cables:

P_loss = (75 A)^2 * 20.0 Ω
P_loss = 112500 W

Therefore, the power loss in the cables is 112500 W or 112.5 kW.

Where:
- P_loss is the power loss in the cables.
- I is the current flowing through the cables.
- R is the total resistance of the cables.

First, you need to find the current (I) flowing through the cables using the power (P) and voltage (V) provided:

P = VI

Given:
- Power (P) = 3.0 kW = 3000 watts
- Voltage (V) = 1.5 kV = 1500 volts

Now, we can rearrange the formula to find the current (I):

I = P / V
I = 3000 W / 1500 V
I = 2 A

Now that you have the current, you can calculate the power loss:

Power Loss (P_loss) = I^2 * R
P_loss = (2 A)^2 * 20.0 Ω
P_loss = 4 A^2 * 20.0 Ω
P_loss = 80.0 W

So, the power loss in the cables is 80.0 watts.