In: Physics

An electric eel develops a potential difference of 500 V, driving a current of 0.90 A for a 1.0 ms pulse.

An electric eel develops a potential difference of 500 V, driving a current of 0.90 A for a 1.0 ms pulse.
A.Find the power of this pulse.
B. Find the total energy of this pulse.
C.Find the total charge that flows during the pulse.

Solutions

Expert Solution

Concepts and reason

The concepts used to solve this problem are electric power, electric energy, and electric charge. Initially, the power of the pulse can be calculated by using the relation between the current, potential difference, and pulse power. Then, the total energy of the pulse can be calculated by using the relation between power and time. Finally, the charge that flows during the pulse can be calculated by current and time.

Fundamentals

Electric current is defined as the rate of flow of charge (electrons) in a wire. The expression for the power of the pulse is, $$P=I V$$

Here, $$P$$ is the power of the pulse, $$I$$ is current, and $$V$$ is the potential difference. The expression for the total energy is, $$E=P t$$

Here, $$E$$ is the total energy, and $$t$$ is the time. The expression for the charge is, $$Q=I t$$

Here, $$Q$$ is the charge.

(A) The expression for the power is,

$$P=I V$$

Substitute $$0.90 \mathrm{~A}$$ for $$I$$ and $$500 \mathrm{~V}$$ for $$V$$, $$P=(0.90 \mathrm{~A})(500 \mathrm{~V})$$

$$=450 \mathrm{~W}$$

The power of the pulse is usually produced by the electric generators through an electric power grid, and the commercially used electric power is kilowatt-hour.

(B) The expression for the energy is, $$E=P t$$

Substitute $$450 \mathrm{~W}$$ for $$P$$ and $$1.0 \mathrm{~ms}$$ for $$t$$,

$$E=(450 \mathrm{~W})\left[(1.0 \mathrm{~ms})\left(\frac{1 \times 10^{-3} \mathrm{~s}}{1 \mathrm{~ms}}\right)\right]$$

$$=0.45 \mathrm{~J}$$

Electric energy is the most convenient form of energy for human usage. It is impossible to store it in a larger quantity. Thus, the energy of the pulse depends on the power of the pulse and time.

(C) The expression for the charge is, $$Q=I t$$

Substitute $$0.90 \mathrm{~A}$$ for $$I$$ and $$1.0 \mathrm{~ms}$$ for $$t$$, $$Q=(0.9 \mathrm{~A})(1.0 \mathrm{~ms})\left(\frac{1 \times 10^{-3} \mathrm{~s}}{1.0 \mathrm{~ms}}\right)$$

$$=9 \times 10^{-4} \mathrm{C}$$

The electric charges create the electric field, and the charge is quantized. It is the integer multiples of individual small units, and it is denoted by e. Thus the charge depends on the current and time.

Part A

The power of the pulse is $$\mathbf{4 5 0} \mathbf{W}$$.

Part B

The energy of the pulse is $$\mathbf{0 . 4 5} \mathbf{J}$$.

Part c

The charge transferred during the pulse is $$9 \times 10^{-4}$$ C.