Concept explainers
The ranking of the given actions in terms of the change in current from greatest increase to the greatest decrease.
Answer to Problem 3OQ
The ranking of current in decreasing order is given by
Explanation of Solution
Write the expression for the Ohm’s Law.
Here,
Write the expression for the power in terms of voltage.
Here,
Write the expression for the resistance.
Here,
Write the expression for the current in terms of potential difference.
Here,
Write the expression for the resistance of the wire in terms of temperature.
Here,
Case (a):
Substitute
Substitute
Substitute
Therefore, the current is
Case (b):
Rearrange equation (II) to find voltage.
Write the expression for the ratio of the voltages at power
Substitute
Substitute
Therefore, the value of current for triple power is
Case (c):
Substitute equation (III) in equation (I) to find
Substitute
Write the expression for voltage
Write the expression for the ratio of
Substitute
Therefore, the current is
Case (d):
Substitute equation (III) in equation (I) to find
Write the expression for voltage
Write the expression for the ratio of voltage
Substitute
Therefore, then current is
Case (e):
From equation (V), it is clear that resistance is proportional to temperature
Hence, when temperature is doubled, the resistance is also doubled.
The ratio of voltages from equation (I) is given by:
Substitute
Therefore, the current is
Conclusion:
Therefore, the ranking of current in the decreasing order is given by
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Chapter 27 Solutions
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