2. Suppose you had a case where Rx is 1000 times as great as Ra and Rv is about

Question

2. Suppose you had a case where Rx is 1000 times as great as Ra and Rv is about equal to Rx. Which connection (C or D) would be best to use if you planned to make no correction. Why? Resistance Measurement 8-2 NOTE: The DMM used in this experiment has been altered to have a high internal resistance for the 20 milliampere scale. This was done to accentuate the affects we are trying to in this laboratory. Unaltered DMMs have much smaller resistance for the ammeter section, but the effects explored in this lab are still present in an meter. v is a voltmeter, A an ammeter, and RI a variable resistor. Rx Consider the circuit shown, where is a resistor of unknown size, and the resistance we wish to measure. Power Figu lt might seem that all one need do is to use the meter readings for V and I, then calculate a nominal value R VII. often this nominal value is only reasonably correct. The result is quite accurate when the resistance of the voltmeter R and the resistance ofthe ammeter R, meet the conditions: R. Rr and R, Rr. There are occasions when one cannot meet both conditions, particularly for high precision measurements. Consideration of the circuit diagram indicates that the current read by the ammeter is the sum of the current in Rx and in V. We are really interested in the current in R.. but the ammeter reading is too large by the amount of current through the voltmeter, I, If the resistance of the voltmeter is known we can calculate the current in the voltmeter, I, VIR., where Vis the value of the voltmeter reading at the time of measurements. When the voltmeter lead is moved from point C to D, as in Figure 2, the current read by the meter is exactly the current through Rx, but now the voltmeter reading is too large by the amount of voltage drop across the ammeter The voltage drop across the ammeter is given by V, I R,, where I is the current as read by the ammeter at the time of the measurement. Power I L Supply MMA, Figure 2 ts of a long the resistan urrent flows Refer t will need cond corre ge of the sd values These ck up ac t mu to ma V is a

Explanation / Answer

Before solving this question, please note the below point.

1. In ideal case resistance of a ameater is 0 (zero) so that all the current would pass through it and it would give the correct measure of current. In real case also, ameater resistance should be kept as small as possible.

2. In ideal case, resistance of the voltmeter is infinite so that no current would pass through it and it would give the correct measure of volatge across any load or resistance.

Now, in 1st question, Rv is 1000 times as greater as Rx and Ra is about equal to Rx. So it means that resistance of voltmeter is very large than the load resistance across which it is connected. Under this condition, almost all the current would pass through the Rx as its resistance is less than Rv. In this case Voltmeter would give correct volatge value across the load resistance i.e. Rx. Since Rx and Ra are nearly equal, hence full current would be flow through ameter also and it would give us correct result. Under this condition both connection C and D would work well and we would able to get the correct reading from voltmeter and ameter.

In 2nd question, Rx is 1000 times as greater than Ra and Rv is about to equal Rx. So in this case if connection D is used then neither the voltage nor the current would measue with accuracy as resistance of voltmeter is less than the load resistace and load resistance is in series with ameter. It means considerable amount of current is flow through voltmeter also and less amount of current will flow through Rx and ameter. If we use connection C here, voltmeter reading is still not give us correct reading as it resistance is less than Rx but in this case we are able to get the correct ameter reading as currect will divided between Rx and voltmeter only after when current will pass the ameter.

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