In the circuit shown, the internal resistance of the battery can be considered negligible.
a. What is the equivalent resistance of the two-resistor parallel combination?
b. What is the total current flowing through the battery?
c. What is the voltage drop across the 12-ohm resistor?
d. What is the voltage drop across the 15-ohm resistor?
e. What is the current flowing through the 15 Ω resistor?
f. What is the power dissipated in the 12 Ω resistor?
g. Is the current flowing through the 12 Ω resistor greater or less than that flowing through the 15 Ω resistor? Explain.
(a)
The equivalent resistance of the two parallel resistors.
Answer to Problem 1SP
The equivalent resistance of the two parallel resistors is
Explanation of Solution
Given info: The given circuit is shown below.
In the given circuit the resistances
Write the formula for the equivalent resistance of two resistances connected in parallel.
Here,
Substitute
Conclusion:
The equivalent resistance of the two parallel resistors is
(b)
The total current flowing in the circuit.
Answer to Problem 1SP
The total current through the circuit is
Explanation of Solution
Given info: The given circuit is shown below.
In the given circuit the resistances
Write the formula for the total resistance of the circuit.
Here,
Write the formula for the total current in the circuit.
Here,
Substitute the expression of
From section (a) the equivalent resistance of the two parallel resistances is
Substitute
Conclusion:
The total current through the circuit is
(c)
The voltage drop across
Answer to Problem 1SP
The voltage drop across
Explanation of Solution
Given info: The given circuit is shown below.
In the given circuit the resistances
The voltage of the battery will get distributed among the
Write the formula for the voltage across the
Here,
From section (a) the equivalent resistance of the parallel connection is
Substitute
Conclusion:
The voltage drop across
(d)
The voltage drop across
Answer to Problem 1SP
The voltage drop across
Explanation of Solution
Given info: The given circuit is shown below.
In the given circuit the resistances
The voltage of the battery will get distributed among the
The voltage drop across
Write the formula for the voltage across the parallel connection of
Here,
From section (c) the voltage across the series resistor is
Substitute
Conclusion:
The voltage drop across
(e)
The current flowing through
Answer to Problem 1SP
The current flowing through
Explanation of Solution
Given info: The given circuit is shown below.
In the given circuit the resistances
Write the formula for current.
Here,
The voltage drop across
Substitute
Conclusion:
The current flowing through
(f)
The power dissipated in
Answer to Problem 1SP
The power dissipated in
Explanation of Solution
Given info: The given circuit is shown below.
In the given circuit the resistances
Write the formula for power.
Here,
From section (c) the voltage drop across
Substitute
Conclusion:
The power dissipated in
(g)
Whether the current through
Answer to Problem 1SP
The current through
Explanation of Solution
Given info: The given circuit is shown below.
In the given circuit the resistances
Since the current is a conserved quantity, in the given circuit, the current through
Conclusion:
The current through
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