Two resistors, one having a resistance of, are connected in series to produce a total resistance of . (a) What is the value of the second resistance? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?
(a)The value of the second resistance is.
(b)Value of the second resistor is negative.
(c)Resistance of the series is less than the resistance of the single resistor.
The resultant resistance of series combination resistors is given as,
Here, is the resultant resistance for series combination, and are the resistances of the resistors connected in series.
Resistors value in series adds up. That means that:
Therefore, the value of the second resistance is.
The unreasonable result is: negative value of the second resistor.
The assumptions are unreasonable or inconsistent is, resistance of the series is less than the resistance of the single resistor.
A ammeter is placed in series with a resistor in a circuit. (a) Draw a circuit diagram of the connection. (b) Calculate the resistance of the combination. (c) If the voltage is kept the same across the combination as it was through the resistor alone, what is the percent decrease in current? (d) If the current is kept the same through the combination as it was through the resistor alone, what is the percent increase in voltage? (e) Are the changes found in parts (c) and (d) significant? Discuss.
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