2501 Current

  • A current is any motion of charge from one region to another.

The Direction of Current Flow

Exercises

7, 8

25.7 The current in a wire varies with time according to the relationship I=55A−(0.65A/s2)t2I = 55 A - (0.65 A/s^2 ) t^2. (a) How many coulombs of charge pass a cross section of the wire in the time interval between t = 0 and t = 8.0 s? (b) What constant current would transport the same charge in the same time interval?

Solution

a. The total charge is

q=∫08.0Idt=(55t−0.653t3)∣08.0=329.1C\begin{aligned} q &= \int_0^{8.0} Idt\\ &= (55t - \frac{0.65}{3}t^3) \vert_0^{8.0}\\ &= 329.1 C \end{aligned}

b. The constant current that would transport the same charge in the same time interval is

I=qt=329.18=41.1A\begin{aligned} I & =\frac{q}{t} = \frac{329.1}{8} = 41.1 A \end{aligned}

25.8 Current passes through a solution of sodium chloride. In 1.00 s, 2.68×10162.68 \times 10^{16} Na+ ions arrive at the negative electrode and 3.92×10163.92 \times 10^{16} Cl- ions arrive at the positive electrode. (a) What is the current passing between the electrodes? (b) What is the direction of the current?

Solution

a. The charge on a proton or an electron is 1.6×10−19C1.6 \times 10^{-19}C. The total charge can be calculated by

Q=(2.68×1016+3.92×1016)×1.6×10−19C=1.056×10−2C\begin{aligned} Q &= (2.68 \times 10^{16} + 3.92 \times 10^{16}) \times 1.6 \times 10^{-19}C\\ &= 1.056 \times 10^{-2}C \end{aligned}

The formular for current is

I=Qt=1.056×10−2C1.00s=1.056×10−2A\begin{aligned} I &= \frac{Q}{t} = \frac{1.056 \times 10^{-2}C}{1.00s}\\ &= 1.056 \times 10^{-2} A \end{aligned}

b. The direction of the current is from positive electrode to negative electrode.