How long should a current of 2.5A (amperes) flow through a conductor with a resistance of 18 ohms and so that 81kJ of energy would be released in it?
We translate the values from given to the SI system:
Q = 81 kJ = 81000 J.
The energy released in the conductor when an electric current passes through it:
Q = P * τ
Formula for determining electrical power:
P = U * I
According to Ohm’s law, the amount of current is directly proportional to the applied voltage and inversely proportional to its resistance:
I = U / R
U = I * R
Substitute into the expression for the power:
P = U * I = I * R * I = I² * R
Substitute in the expression for the energy:
Q = P * τ = I² * R * τ =
Let us express time from this expression:
τ = Q / (I² * R)
Substitute the numerical values and find the time:
τ = Q / (I² * R) = 81000 / (2.5² * 18) = 720 s.
Answer: 720 sec or 12 min is needed.
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