Four resistors are connected to a battery as shown in Figure P27.15. (a) Determine the potential difference across each resistor in terms of ε. (b) Determine the current in each resistor in terms of I. (c) What If? If R3 is increased, explain what happens to the current in each of the resistors. (d) In the limit that R3 → ∞, what are the new values of the current in each resistor in terms of I, the original current in the battery?
Figure P27.15
(a)
The potential difference across each resistor in terms of
Answer to Problem 15P
The potential difference across
Explanation of Solution
The resistors
Figure (1)
Formula to calculate the resistance across the circuit when resistors
Here,
Substitute
Thus, the resistance across the circuit when resistors
The resistors
Figure (2)
Formula to calculate the resistance when the resistors are connected in parallel is,
Here,
Substitute
Thus, the value of the resistance when the resistors are connected in parallel is
The resistors
Figure (3)
Formula to calculate the equivalent resistance across the circuit is,
Here,
Substitute
Thus, the equivalent resistance across the circuit is
The equivalent resistance is shown in the figure 4.
Figure (4)
Formula to calculate the current across the circuit is,
Here,
Substitute
Thus, the current across the circuit is
Formula to calculate the voltage across the
Here,
Substitute
Thus, the voltage across the
Thus, the voltage across the
Formula to calculate the voltage across the
Here,
Substitute
Thus, the voltage across the
Formula to calculate the current across the
Here,
Substitute
Thus, the current across the
Formula to calculate the current across the
Here,
Substitute
Thus, the current across the
Formula to calculate the voltage across the
Here,
Substitute
Thus, the voltage across the
Formula to calculate the voltage across the
Here,
Substitute
Thus, the voltage across the
Conclusion:
Therefore, the potential difference across
(b)
The current in each resistor in terms of
Answer to Problem 15P
The current across
Explanation of Solution
Formula to calculate the value of
Substitute
Thus, the value of
Formula to calculate the current across the
Here,
Substitute
Substitute
Thus, the current across the
Formula to calculate the current across the
Here,
Substitute
Substitute
Thus, the current across the
Formula to calculate the current across the
Here,
Substitute
Substitute
Thus, the current across the
Formula to calculate the current across the
Here,
Substitute
Substitute
Thus, the current across the
Conclusion:
Therefore, the current across
(c)
The effect in the current in each of the resistors, if
Answer to Problem 15P
The value of current across
Explanation of Solution
If the value of the
Since, the current remains same in series combination. So, the value of current across
If the value of the
Thus, the current across the
Conclusion:
Therefore, the value of current across
(d)
The new values of the current in each resistor in terms of
Answer to Problem 15P
The current across
Explanation of Solution
If
Here,
The resistors
Formula to calculate the resistance across the circuit when resistors
Here,
Substitute
Thus, the resistance across the circuit when resistors
From equation (11), the value of
From equation (12), formula to calculate the current across the
Here,
Substitute
Thus, the current across the
As the resistors
Here,
Thus, the original current in the battery is
Conclusion:
Therefore, the current across
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Physics for Scientists and Engineers with Modern Physics
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