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Three resistors are connected to a 12-V battery as shown. The internal resistance of the battery is negligible.
a. What is the total resistance in the circuit?
b. What is the current coming from the battery?
c. What is the current through the 15 Ω. resistance?
d. Does this same current flow through the 25 Ω resistance?
e. What is the voltage difference across the 20 Ω resistance?
(a)
![Check Mark](/static/check-mark.png)
The total resistance of the circuit.
Answer to Problem 9E
The equivalent resistance of the circuit is
Explanation of Solution
Given info: The voltage of the battery is
Write the formula for the equivalent resistance when three resistances are connected in series.
Here,
Substitute
Conclusion:
The equivalent resistance of the circuit is
(b)
![Check Mark](/static/check-mark.png)
The current in the circuit.
Answer to Problem 9E
The current in the circuit is
Explanation of Solution
Given info: The voltage of the battery is
Write the formula for the equivalent resistance when three resistances are connected in series.
Here,
Write the formula for the current in the circuit.
Here,
Substitute
Conclusion:
The current in the circuit is
(c)
![Check Mark](/static/check-mark.png)
The current through the resistor
Answer to Problem 9E
The current through the
Explanation of Solution
Given info: The voltage of the battery is
When resistors are connected in series, the path for current is same. So the current flowing through all the elements which are in series with each other is same.
In the given circuit, the three resistances are connected in series. So the current through each resistor will be same which will be equal to the current coming from the battery.
In the section (b), the current from the battery was found out to be
Conclusion:
The current through the
(d)
![Check Mark](/static/check-mark.png)
Whether the current flowing through
Answer to Problem 9E
The current flowing through
Explanation of Solution
Given info: The voltage of the battery is
When resistors are connected in series, the path for current is same. So the current flowing through all the elements which are in series with each other is same.
In the given circuit, the three resistances are connected in series. So the current through each resistor will be same which will be equal to the current coming from the battery.
Thus the current flowing through
Conclusion:
The current flowing through
(e)
![Check Mark](/static/check-mark.png)
The voltage across
Answer to Problem 9E
The voltage across
Explanation of Solution
Given info: The voltage of the battery is
Write the formula for the voltage across a resistor in series with two other resistors.
Here,
Substitute
Conclusion:
The voltage across
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Chapter 13 Solutions
Physics of Everyday Phenomena
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