實驗5: 安培計、伏特計和歐姆計 Expt. 5: Ampere meter, Voltmeter & Ohmmeter (課本實驗19/Expt. 19 in Textbook) 目 的: 瞭解安培計、伏特計和歐姆計的基本構造 並用已分別測量電路中的電流、電壓和電阻 熟悉簡單電路的特性和基本測量

What is a meter? http://www.allaboutcircuits.com/vol_1/chpt_8/1.html Table of Contents: What is a meter? Voltmeter design Voltmeter impact on measured circuit Ammeter design Ammeter impact on measured circuit Ohmmeter design High voltage ohmmeters Multimeters Kelvin (4-wire) resistance measurement Bridge circuits Wattmeter design Creating custom calibration resistances

What is a Meter? http://www.allaboutcircuits.com/vol_1/chpt_8/1.html Meter: A meter is any device built to accurately detect and display an electrical quantity in a form readable by a human being. Digital Meter - their readable display is in the form of numerical digits. Movement Meter - Older designs of meters are mechanical in nature, using some kind of pointer device to show quantity of measurement. In either case, the principles applied in adapting a display unit to the measurement of (relatively) large quantities of voltage, current, or resistance are the same.

The Display Mechanism of a Meter It often referred to as a movement, borrowing from its mechanical nature to move a pointer along a scale so that a measured value may be read. Though modern digital meters have no moving parts, the term "movement" may be applied to the same basic device performing the display function. Most mechanical movements are based on the principle of electromagnetism: 1. The electric current through a conductor produces a magnetic field perpendicular to the axis of electron flow. The greater the electric current, the stronger the magnetic field produced. 2. If the magnetic field formed by the conductor is allowed to interact with another magnetic field, a physical force will be generated between the two sources of fields. 3. If one of these sources is free to move with respect to the other, it will do so as current is conducted through the wire, the motion (usually against the resistance of a spring) being proportional to strength of current.

Most meter movements are polarity-sensitive, one direction of current driving the needle to the right and the other driving it to the left. Some meter movements have a needle that is spring-centered in the middle of the scale sweep instead of to the left, thus enabling measurements of either polarity: Passing AC through the D'Arsonval meter movement causes useless flutter of the needle.

Galvanometers (檢流計) -The first meter movements Be usually designed with maximum sensitivity in mind. A very simple galvanometer may be made from a magnetized needle (such as the needle from a magnetic compass) suspended from a string, and positioned within a coil of wire. Current through the wire coil will produce a magnetic field which will deflect the needle from pointing in the direction of earth's magnetic field. Now, the term "galvanometer" usually refers to any design of electromagnetic meter movement built for exceptional sensitivity. Practical electromagnetic meter movements can be made now where a pivoting wire coil is suspended in a strong magnetic field, shielded from the majority of outside influences. Such an instrument design is generally known as a permanent-magnet, moving coil, or PMMC movement:

An Antique String Galvanometer

Most meter movements are polarity-sensitive, one direction of current driving the needle to the right and the other driving it to the left. Some meter movements have a needle that is spring-centered in the middle of the scale sweep instead of to the left, thus enabling measurements of either polarity: Passing AC through the D'Arsonval meter movement causes useless flutter of the needle.

達松發可動線圈 D’Arsonval movement Coil 原理(Principle)：利用檢流計(galvanometer, G)設計 1. 安培計(ammeter, A) 2. 伏特計(voltmeter, V) 3. 歐姆計(ohmmeter, O) (參考三用電表) 1. 指針(Needle) 2. 空氣隙(Air Gap) 3. 永久磁鐵(Permanent Magnet) 4. 螺線彈簧(Solenoidal Coil) 5. 轉動線圈(Rotating Coil) 6. 轉動軸心(Pivot Rotating Coil) 7. 軟鐵心(Soft-Iron Core) 8. 均勻輻射狀磁場(Uniform Radial Field)

(Operation Principle of D’Avsonval movement coil galvanometer) 達松發可動線圈檢流計的工作原理 (Operation Principle of D’Avsonval movement coil galvanometer) 電流 I 通過轉動線圈(coil)時, 產生磁矩 m = NIA (圈數N,面積A), 永久磁鐵之均勻輻射磁場對 m 施一力矩(torque)  = m x B = NIAB (f = 90o), 3. 使線圈轉動, 淨角位移  與螺線彈簧恢復力矩 ’ 成平衡: = mB = NIAB = k = ’ 4. 角位移與電流正比 I = (k/NAB)  

A. 電流測量: 安培計(Ampere meter)/電流計(Ammeter) 利用檢流計(G)(線圈電阻Rc)及一個小的 並聯電阻(Rp << Rc)設計安培計。 安培計有效電阻 RA = RP // Rc = RpRc/(Rp+Rc) ~ Rp Vab = IcRc = IpRp I = Ic + Ip = Ic(1 + Rc/Rp)  小的並聯電阻 Rp : 增加電流測量範圍, 減少安培計有效電阻RA 若線圈電阻 Rc = 1.2 k, 最大偏轉電流 Ic(max) = 50 mA 如 Rp = 12  I(max) = 101 Ic(max) = 5.05 mA RA = 12 x 1200/1212 ~ 12 

Electrostatic Meter Movements Unfortunately, the force generated by the electrostatic attraction is very small for common voltages. In fact, it is so small that such meter movement designs are impractical for use in general test instruments. Typically, electrostatic meter movements are used for measuring very high voltages (many thousands of volts). One great advantage of the electrostatic meter movement, however, is the fact that it has extremely high resistance, whereas electromagnetic movements (which depend on the flow of electrons through wire to generate a magnetic field) are much lower in resistance. As we will see in greater detail to come, greater resistance (resulting in less current drawn from the circuit under test) makes for a better voltmeter.

B. 電壓測量: 伏特計(V, Voltmeter)/電壓計(Potentometer) 利用檢流計(G)(線圈電阻Rc)及一個 大的串聯電阻(Rs >> Rc)設計伏特計。 伏特計有效電阻 RV = Rc + Rs Vab = Ic(Rc + Rs) 大的串聯電阻Rs: 增加電壓測量範圍及伏特計有效電阻RV 例: 若線圈電阻 Rc = 1.2 k, 最大偏轉電流 Ic(max) = 50 mA V(max) = 60 mV 如 Rs = 120 k RV = 1200 + 120000 ~ 120 k V(max) ~ 6 V

歐姆計(O, Ohmmeter)/電阻計(Resistance meter) 利用檢流計(G)(線圈電阻Rc), 一個零點串聯電阻(Rs0)及內建串聯電池(或直流電源供應器)電動勢(e)設計歐姆計： 1. x, y二點短路(R = 0) 選擇 Rs0 使檢流計達最大電流 Ic = Ic(max) (指針最大偏轉) = /(Rc + Rs0) 2. x, y二點斷路(R = ),無電流 Ic = 0 (零點) 3. x, y接待測電阻R Ic = /(Rc + Rs0 + R) R = /Ic – (Rc + Rs0) = (Rc + Rs0)[Ic(max)/Ic – 1]

實驗流程: A. 安培計 1. 用以測量電路電流, 需與電路串聯 2. 安培計內電阻RA 需遠小於電路上的總等校電阻 RA << R，以使通過安培計的電壓 VA = IRA ~ 0 。 B. 伏特計 1. 測量電路電位降用, 需與待測元件並聯 2. 伏特計內電阻 RV 需極大於待測元件電阻 RV >> R， 以使通過伏特計之電流 Ic = IR/RV ~ 0