Answer :
After powering the circuit for 1 hour, the battery has 75 kJ - 12.96 kJ = 62.04 kJ of energy left.
To solve this problem, we first need to calculate the amount of energy supplied by the battery to the circuit in one hour. This can be done using the formula:
Energy = Power x Time
Since the battery supplies a constant voltage of 6 volts to the circuit, we can use Ohm's Law (V = IR) to calculate the current flowing through the circuit. Assuming the resistance of the circuit is known, we can use the formula:
Power = Voltage x Current
Once we have the power supplied by the battery, we can use it to calculate the energy supplied in one hour:
Energy = Power x Time = (Voltage x Current) x Time
Now, let's assume that the circuit has a resistance of 10 ohms. Using Ohm's Law, we can calculate the current flowing through the circuit as:
Current = Voltage / Resistance = 6 V / 10 Ω = 0.6 A
Using the formula for power, we can calculate the power supplied by the battery as:
Power = Voltage x Current = 6 V x 0.6 A = 3.6 W
Finally, we can calculate the energy supplied by the battery in one hour as:
Energy = Power x Time = 3.6 W x 1 hour = 3.6 Wh
Note that 1 Wh (watt-hour) is equivalent to 3600 joules (J), so we can convert the energy supplied by the battery to joules as:
Energy = 3.6 Wh x 3600 J/Wh = 12,960 J = 12.96 kJ
Therefore, after powering the circuit for 1 hour, the battery has 75 kJ - 12.96 kJ = 62.04 kJ of energy left.
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The energy stored in the battery is 75 kJ = 75,000 J.
To find the energy left after powering the circuit for 1 hour, we need to convert 1 hour to seconds (3600 seconds) and then subtract the energy used by the circuit from the total energy of the battery:
Energy left = Total energy - Energy used
Energy left = 75,000 J - (current supplied x time)
Energy left = 75,000 J - (6 V x 1 hour)
Energy left = 75,000 J - 6 x 3600 J
Energy left = 75,000 J - 21,600 J
Energy left = 53,400 J
The battery starts with 75,000 J of energy and has 53,400 J left after powering the circuit for 1 hour.
