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DIRECT CURRENT MEASUREMENTS In this laboratory, use the white and black milliammeter Ammeter The moving coil galvanometer, from which the milliammeter of this experiment is derived, contains a pivoted coil of fine wire through which a current passes. The magnetic interaction between the magnetic field set up by this current and the magnetic field of the permanent magnet housed in the meter casing results in movement of the coil against a hair-spring. The resulting displacement is shown by the meter needle against a scale. The sensitivity of a particular meter movement is the current required for fullscale deflection. Very sensitive meters deflect full-scale for currents in the order of 10 to 100 µA. Meter movements are usually rated by current and resistance. A typical rating is 1 mA, 50 Ω. For a given meter, the deflection is proportional to the coil current. Since this current is proportional to the coil voltage, the deflection is also proportional to this voltage. For an illustration, consider a meter that deflects full-scale for a coil current of 1.0 mA, and that has a coil resistance of 20 Ω. The corresponding coil voltage is VT = RmImf = 20(0.001) = 20 mV In which Rm is the movement resistance, and Imf is the current required for full-scale deflection. The range of an ammeter is the current that causes full-scale deflection. Normally, a scale is not calibrated beyond the region for linear deflection nor for a current that would damage the fine wire in the coil movement. The range can be extended and at the same time the equivalent resistance reduced by connecting a resistor Rsh of low resistance in parallel with the meter terminals, as is shown in Fig. 3.1. Resistor Rsh is known as the shunt resistor. Incidentally, the expression “in shunt with” is sometimes used to mean “in parallel with.” Fig. 3.1 + VT + I A VT I Ish Rsh Imf Rm An expression will now be derived for extending the range of an ammeter for the measurement of a current I greater than Imf. With reference to Fig. 3.1, I = Ish + Imf and VT = RshIsh = RmImf Where I = desired range of new ammeter. Thus, R sh = I mf I sh I mf Rm = I − I mf Rm Rm = I −1 I mf For an illustration, suppose the previously considered meter is to be converted to an ammeter with a range of 0 to 100 mA. Here, I = 100 mA, Imf = 1 mA, and Rm = 20 Ω. Then, R sh = Rm 20 = = 0.202 Ω I 100 / 1 − 1 −1 I mf With Rsh = 0.202Ω in parallel with the original meter, the result is a low resistance ammeter with the desired range of 0 to 100 mA. Voltmeter As mentioned, an ideal voltmeter has an infinite input resistance, while a practical voltmeter has a large input resistance—the larger the better. If the meter being considered is used as a voltmeter, its range is only 0 to 20mV. This range can be extended, and at the same time the equivalent resistance increased. This is done by connecting a resistor of large resistance Rs, called a multiplier resistor, in series with the moving coil as is shown in Fig. 3.2. + + Im VT Rs VT V - Im Rm - Fig. 3.2 For an illustration, suppose a voltmeter is to be designed with this meter and that the new voltage range is to be from 0 to 20V. Thus, the current through the meter must be 1 mA when 20V is applied to the terminals to obtain a full-scale deflection. From Fig. 3.2, and with Im = Imf, VT = (Rm + Rs)Imf, from which Rs = VT 20 − Rm = − 20 = 19 ,980 Ω. I mf 0.001 Thus, a multiplier resistor of approximately 20kΩ increases the resistance of the voltmeter and extends the range to 20V maximum. Incidentally, from the final equation it can be seen that a more sensitive meter movement (smaller Imf) would result in a better voltmeter. Ohmmeter The common ohmmeter is not a precision instrument, but it is useful for the rapid measurement of resistance. It consists of a meter, a series resistor, and a series dc voltage source which is often a flashlight cell. An ohmmeter is illustrated in Fig. 3.3. x Rs Im Rv Rm Rx Vs y Fig. 3.3 The resistor, the resistance Rx of which is to be measured, is connected to terminals x and y. The series resistance Rs is chosen such that when terminals x and y are short-circuited (Rx = 0), the meter deflects full-scale. When the terminals x and y are open-circuited, the meter shows no deflection. Therefore, a finite nonzero value of Rx will give a fraction of full-scale deflection. Thus, the meter scale can be calibrated to “read” the resistance Rx. A small variable resistor Rv is included in the ohmmeter circuit to permit zeroing of the ohmmeter when the x and y terminals are short-circuited. Due to aging of the battery and an increase in its internal resistance, the voltage available at its terminals decreases with time and is offset by reducing the resistance Rv Because the meter deflection is proportional to the coil current I, deflection ∝ I = in which “ ∝ ” indicates “is proportional to.” Vs , R x + ( R s + Rv + Rm ) Procedure: 1. The circuit of Fig. 3.4 will be used in determining Rm, the resistance of the milliammeter between the ground terminal and the positive terminal. On the back of the meter, there are two metal tabs (don’t confuse the screws for tabs), where the left tab is marked with “+” for positive terminal). On the front of the milliammeter, one can see that full-scale deflection occurs at 1 mA. For the ammeter A, use a multimeter on the DC amp setting. Use a decade box for Rsh so that an accurate value of Rsh can be obtained. The accuracy of this resistance largely determines the accuracy to which Rm can be measured. A 2.2 k Ω I Vs Im Ish Rm Rsh Fig. 3.4 a) Construct the circuit of Fig. 3.4 b) Set Rsh = 5000 Ω. Then, with the multimeter on the 100-200mA scale, begin with the source voltage equal to zero (Vs = 0). Slowly increase Vs until the milliammeter reads full-scale deflection. c) For an accurate measurement of Rm, the smallest possible value of Rsh must be used. To find this value, showly reduce Rsh. Each time its value is decreased, raise the power-supply voltage Vs until full-scale deflection is reached again. Eventually, Rsh will be such a small value that full-scale deflection cannot be obtained. Then, raise Rsh to the desired value. d) Use the determined value of Rsh, the value of Imf (1 mA), and the value of I measured by the multimeter to solve for Rm from I Rm = Rsh( - 1) I mf which is from the expression derived in the ammeter section. 2. Design and build an ammeter having a range of 0-100mA. Use it to measure all the branch currents in the circuit of Fig. 3.5 for Vs = 11V. (The new ammeter should be placed in series in a branch for current measurement.) Vs Fig. 3.5 Use the multimeter as a standard ammeter to check the ammeter readings. Calculate the percentage error for the three different current readings. The source voltage Vs may be adjusted to test the range design of 100 mA, but be sure to document any change and be sure not to overload the ammeter when measuring. 3. Design and build a voltmeter having a range of 0-10V. Use it to measure all the voltages in the circuit of Fig. 3.6 for Vs = 10V. Vs Fig. 3.6 Use the multimeter as a standard voltmeter to check the constructed voltmeter readings. Calculate the percentage error for the three voltage readings, including the source voltage. Explain the poor results, if any. 4. Design and build an ohmmeter that deflects half-scale when measuring an 8.2kΩ resistor, and that has full-scale deflection for a short circuit. Omit Rv in Fig. 3.3. Also, use a variable dc power supply instead of a battery. Adjustment of the power supply to the correct voltage is part of the design problem. Vs and Rs should both be varied to obtain the desired conditions for half- and full-scale deflections. Make three measurements above and three measurements below half-scale deflection and note the corresponding deflection of the meter. Make sure that the measurements include the extreme ends of the deflection. Draw a graph of Rx versus the deflection of the meter. Is the deflection a linear function of resistance?