欧姆定律

欧姆定律指出，电阻器之间的电压差与电阻的电流成正比。比例的常数是电阻，R. The governing equation is shown to the left below, while a typical symbolic representation of a resistor is shown to the right below.

$$ v（t）= r \ cdot（t）$$

Wherev(t)是电阻器上的电压i(t)is the current through the resistor. Ohm's law can also be written as:

$i(t) = v(t)R$ or $R = v(t)i(t)$

最后两个表达式只是第一个的重排。

The units of resistance are ohms (abbreviated Ω). Resistances are commonly on the order of thousands to millions of ohms. Thousands of ohms are represented as kilo-ohms (abbreviated kΩ), while millions of ohms are represented as mega-ohms (abbreviated MΩ). Thus, 10,000Ω can be represented as 10k Ω while 2,000,000Ω can be represented as 2 MΩ.

The direction of the current,i(t), relative to the sign of the voltage difference,v(t)，当我们开始数学分析电路时，对我们很重要。请注意，电流是entering the positive电压node in the above figure. This is known as thepassive sign convention. In the passive sign convention, positive current isassumed输入正电压端子。当我们开始数学上建模电路时，我们将稍后强调这个概念。

The important thing to note about Ohm's law is that a resistor's voltage and current through are related by its resistance. As examples, consider the following cases:

• Increasing电阻的电压decreases电流通过电阻，反之亦然。例如，将电阻器跨电阻的电压加倍将电流一半通过电阻器。对于100Ω电阻，该情况的一个具体示例如下所示。

• Increasingthe resistance while keeping the voltage across the resistor constantdecreasesthe current. For example, doubling the resistance will halve the current if the voltage is constant. A specific example of this is shown below.

This property of resistors is often useful in circuit design. Many devices can provide only limited current; if your circuit draws too much current from the device, it can malfunction. Increasing the resistance in your circuit may solve this problem.

1.100Ω电阻的电压是多少？指示图纸上的极性（正和负末端）。
2.What is the voltage across the 2 kΩ resistor? (Note: the “k” prefix stands for “kilo”, or thousands. This is a 2000Ω resistor.) Indicate the polarity (positive and negative terminals) on the drawing.
3.5kΩ电阻的电压是多少？（注意：“ M”前缀代表“ Milli”或千分之一。电流为0.004a。）表示图纸上的极性（正和负末端）。
4.什么是阻力，R, of the resistor?
5.什么是阻力，R, of the resistor?
6。What is the current through the resistor? What direction is it in?
7。What is the current through the resistor? What direction is it in?
8。What is the current through the resistor? What direction is it in?
9.What is the voltage across the 2 MΩ resistor? (Note: the “M” prefix stands for “mega”, or millions. The resistance is 2,000,000Ω. Also, the “µ” prefix on current stands for “micro”, or millionths. The current is 7×10-6A, or 0.000007A.) Indicate the polarity (positive and negative terminals) on the drawing.
10。电阻的电阻是什么？
11.通过电阻器的电压是多少?指示图纸上的极性（正和负末端）。

1. (3A)x(100Ω) = 300V. The positive terminal is to the left, and the negative terminal to the right. (It has to obey the passive sign convention, and current is entering the left terminal.)
2. (0.4A)x(2000Ω) = 800V. The positive terminal is to the right, and the negative terminal to the left. (It has to obey the passive sign convention, and current is entering the right terminal.)
3. (0.004A)x(5000Ω) = 200V. The positive terminal is to the left, and the negative terminal to the right. (It has to obey the passive sign convention, and current is entering the left terminal.)
4. (4V)/(0.002A) = 2000Ω.
5. Trick question; a resistor cannot have current entering the negative voltage terminal.
6. （20V）/（10,000Ω）= 2mA（或0.002a）。电流进入左端。（它必须遵守被动标志公约，正电压在左端。）
7. (3V)/(5,000Ω) = 0.6mA (or 0.0006A). Current enters the right terminal. (It has to obey the passive sign convention, and positive voltage is at the right terminal.)
8. (10v)/(3,000Ω) = 3mA (or 0.003A). Current enters the right terminal. (It has to obey the passive sign convention, and positive voltage is at the right terminal)
9. (0.000007A)x(2,000,000Ω) = 14V. The positive terminal is to the right, and the negative terminal to the left. (It has to obey the passive sign convention, and current is entering the right terminal.)
10. (6V)/(0.000012A) = 500,000Ω (or 500 kΩ).
11. (200,000Ω)x(0.005A) = 1,000V. The positive terminal is to the right, and the negative terminal to the left. (It has to obey the passive sign convention, and current is entering the right terminal.)