a 6.0 kW electric oven is connected to a fuse box by a cable of resistance 0.25 ohms. when the cooker is switched on at full power, a current of 26 A passes through it.
Calculate the potential difference between the two ends of the cable and the power wasted in it because of the heating effect of the current.
What %age of the power supplied to the cable is wasted?
power wasted: I^2 * resistance
Assuming the actual power used by the oven is 6kw, then voltage=6000/26 volts
percent power wasted= powerwasted/(6kw+powerwasted) * 100
To calculate the potential difference between the two ends of the cable, we can use Ohm's Law, which states that V (potential difference) is equal to I (current) multiplied by R (resistance).
Given:
Power of the oven (P) = 6.0 kW = 6000 W
Resistance of the cable (R) = 0.25 ohms
Current passing through the cable (I) = 26 A
Step 1: Calculate the potential difference (V):
V = I * R
V = 26 A * 0.25 ohms
V = 6.5 V
Therefore, the potential difference between the two ends of the cable is 6.5 V.
Step 2: Calculate the power wasted in the cable:
Power (P) = I^2 * R
P = (26 A)^2 * 0.25 ohms
P = 169 W
Therefore, the power wasted in the cable due to the heating effect of the current is 169 Watts.
Step 3: Calculate the percentage of power wasted:
Percentage of power wasted = (Power wasted / Power supplied) * 100
Power supplied = Power of the oven = 6000 W
Percentage of power wasted = (169 W / 6000 W) * 100
Percentage of power wasted ≈ 2.8%
Therefore, approximately 2.8% of the power supplied to the cable is wasted.
To calculate the potential difference, we can use Ohm's Law, which states that the potential difference (V) across a circuit element is equal to the current (I) through the element multiplied by its resistance (R).
Potential Difference (V) = Current (I) * Resistance (R)
In this case, the current passing through the cable is 26 A, and the resistance of the cable is 0.25 ohms.
V = 26 A * 0.25 ohms
V = 6.5 volts
Therefore, the potential difference between the two ends of the cable is 6.5 volts.
To calculate the power wasted in the cable due to the heating effect, we can use the formula:
Power (P) = Current (I)² * Resistance (R)
P = 26 A * 26 A * 0.25 ohms
P = 169 W
Therefore, the power wasted in the cable due to the heating effect is 169 watts.
To calculate the percentage of power supplied to the cable that is wasted, we can use the following formula:
Percentage of Power wasted = (Power wasted / Power supplied) * 100
The power supplied to the cable is given as 6.0 kW (where 1 kW = 1000 watts).
Power supplied = 6.0 kW = 6,000 watts
Percentage of Power wasted = (169 watts / 6,000 watts) * 100
Percentage of Power wasted = 2.82%
Therefore, approximately 2.82% of the power supplied to the cable is wasted.