Practical Circuits | 实用电路

📚 Practical Circuits | 实用电路

Practical circuits form the core of experimental and applied electronics in CIE A-Level Physics. This article covers EMF, internal resistance, potential dividers, Kirchhoff’s laws, power transfer, measuring instruments, sensors and safety considerations. Understanding these ideas helps you design, analyse and troubleshoot real circuits, not just idealised textbook diagrams.

实用电路是 CIE A-Level 物理中实验与应用电子学的核心内容。本文涵盖电动势、内阻、分压器、基尔霍夫定律、功率传输、测量仪表、传感器以及安全注意事项。理解这些概念有助于你设计、分析和排查真实电路，而不仅仅局限于理想化的课本电路图。

1. EMF and Internal Resistance | 电动势与内阻

A real cell has an electromotive force (EMF) E and an internal resistance r. When a current I flows, the terminal potential difference V across the cell is less than the EMF because some energy is converted to heat inside the cell. This so-called lost volts is given by Ir.

真实电池具有电动势 E 和内阻 r。当电流 I 流过时，电池两端的端电压 V 小于电动势，因为部分能量在电池内部转化为热量。这部分损失的电压由 Ir 给出。

V = E − Ir

EMF is defined as the energy transferred per unit charge from chemical or other forms to electrical energy when no current is drawn. Internal resistance arises from the opposition to charge flow within the electrolyte and electrodes.

电动势定义为在没有电流时，将化学能或其他形式的能量转化为电能时每单位电荷所转移的能量。内阻来源于电解质和电极内部对电荷流动的阻碍。

In an open circuit, I = 0, so V = E. Under load, V collapses as I increases; this explains why a battery’s terminal voltage drops when it supplies a large current.

在开路时，I = 0，因此 V = E。在有负载时，随着 I 增大，V 会下降；这解释了为什么电池在提供大电流时端电压会降低。

---

2. Measuring EMF and Internal Resistance | 测量电动势和内阻

A standard method uses a variable resistor, an ammeter and a voltmeter connected across the cell. By changing the resistance, different pairs of I and V are recorded. Plotting V against I gives a straight line of gradient −r and y-intercept E.

标准方法使用一个可变电阻、一个电流表和一个并联在电池两端的电压表。通过改变电阻，记录不同的 I 和 V 数据。绘制 V-I 图可得到一条斜率为 −r、纵截距为 E 的直线。

The intercept on the voltage axis gives the EMF because when I = 0, V = E. The gradient is negative, and its magnitude equals the internal resistance r. A steeper line indicates a larger internal resistance and a poorer battery under load.

电压轴上的截距给出电动势，因为当 I = 0 时，V = E。斜率为负，其绝对值等于内阻 r。线越陡，表示内阻越大，电池在负载下性能越差。

A digital multimeter can also be used, but the high input resistance of a digital voltmeter means it draws negligible current, making open-circuit measurement of EMF accurate.

也可以使用数字万用表，但由于数字电压表的输入电阻很高，它吸取的电流可以忽略不计，因此开路测量电动势较为准确。

---

3. Potential Dividers | 分压器

A potential divider uses two resistors in series to provide a fraction of the input voltage. For resistors R1 and R2 in series across a supply V_in, the output across R2 is given by the ratio of R2 to the total resistance.

分压器利用两个串联电阻来提供输入电压的一部分。对于串联在电源 V_in 两端的电阻 R1 和 R2，R2 两端的输出电压由其电阻与总电阻的比值决定。

V_out = V_in × R₂ / (R₁ + R₂)

If R2 is a variable resistor, the output can be adjusted continuously. This is used in volume controls, brightness controls, and to set reference voltages in sensor circuits.

如果 R2 是可变电阻，输出电压就可以连续调节。这用于音量控制、亮度控制以及在传感器电路中设置参考电压。

A potential divider only works predictably when the load connected across R2 has a very high resistance compared with R2. Otherwise, the load draws current and changes the effective resistance, altering V_out.

只有当连接在 R2 两端的负载电阻远大于 R2 时，分压器才能按照预期工作。否则，负载会吸取电流，改变有效电阻，从而使 V_out 发生变化。

---

4. Potentiometers | 电位器

A potentiometer is a three-terminal device with a sliding contact that can tap any fraction of the total resistance. It is often used as a variable potential divider rather than a simple variable resistor.

电位器是一种三端器件，带有一个滑动触头，可以取出总电阻的任意比例。它通常用作可变分压器，而不是简单的可变电阻。

In precision measurements, a potentiometer can compare an unknown EMF with a known standard cell without drawing current from the unknown source. This null method avoids the effect of internal resistance.

在精密测量中，电位器可以将未知电动势与已知标准电池进行比较，而不会从未知电源吸取电流。这种零平衡法避免了内阻的影响。

When used in practical circuits, a potentiometer provides an adjustable voltage. If wired as a rheostat (using one end and the slider), it acts as a variable resistor, which is common in current-limiting applications.

在实用电路中，电位器提供可调电压。如果作为变阻器接线（使用一端和滑片），它起到可变电阻的作用，这在限流应用中很常见。

---

5. Kirchhoff’s Laws in Practical Circuits | 实用电路中的基尔霍夫定律

Kirchhoff’s current law (KCL) states that the algebraic sum of currents entering any junction is zero. In other words, total current into a junction equals total current out. This is a consequence of conservation of charge.

基尔霍夫电流定律（KCL）指出，流入任一节点的电流代数和为零。也就是说，流入节点的总电流等于流出节点的总电流。这是电荷守恒的结果。

Kirchhoff’s voltage law (KVL) states that the algebraic sum of potential differences around any closed loop is zero. This follows from conservation of energy. In practical circuits, KVL is used to include the internal resistance of cells and voltage drops across components.

基尔霍夫电压定律（KVL）指出，沿任一闭合回路的电位差代数和为零。这是能量守恒的结果。在实用电路中，KVL 用于将电池内阻和各元件上的电压降都考虑进去。

When analysing a multi-loop circuit, choose loop currents and apply KVL to each loop. The simultaneous equations can be solved for the branch currents. This is essential for circuits with more than one source or non-series/parallel connections.

分析多回路电路时，选取回路电流并对每个回路应用 KVL。联立方程可以解出各支路电流。这对于具有多个电源或非串并联连接的电路至关重要。

---

6. Series and Parallel Circuit Characteristics | 串联与并联电路特性

In a series circuit, the current is the same through all components, and the total resistance is the sum of individual resistances. The supply voltage divides across components in proportion to their resistances.

在串联电路中，通过所有元件的电流相同，总电阻等于各电阻之和。电源电压按电阻比例分配到各元件上。

In a parallel circuit, the potential difference across each branch is the same, and the total current is the sum of branch currents. The reciprocal of the total resistance is the sum of the reciprocals of individual branch resistances.

在并联电路中，各支路两端的电位差相同，总电流等于各支路电流之和。总电阻的倒数等于各支路电阻倒数之和。

Household appliances are connected in parallel so that each receives the full mains voltage and can operate independently. If one device fails, the others continue to work. Series connections are avoided because failure of one component would break the whole circuit

Published by TutorHao | A-Level Physics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）