1) The equivalent resistance is [tex]2.73\Omega[/tex]
2) The voltage in the circuit is 120 V
3) The total current in the circuit is 44.0 A
Explanation:
1)
Resistors are said to be in parallel when they have the same potential difference at their terminals.
The formula to calculate the equivalent resistance for three resistors in parallel is:
[tex]\frac{1}{R_T}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}[/tex]
where [tex]R_1, R_2, R_3[/tex] are the resistances of the three resistors.
In this problem, the resistance of each resistor is:
[tex]R_1 = 5.0 \Omega[/tex]
[tex]R_2 = 10.0 \Omega[/tex]
[tex]R_3 = 15.0 \Omega[/tex]
Substituting,
[tex]\frac{1}{R_T}=\frac{1}{5}+\frac{1}{10}+\frac{1}{15}=\frac{11}{30}[/tex]
So the equivalent resistance is
[tex]R_T = \frac{30}{11}=2.73 \Omega[/tex]
2)
In this problem we are told that the three resistors are connected in parallel. This means that their terminals are connected to the same point of the circuit: therefore, this means that they also have the same potential difference across them.
Therefore, the voltage in each branch containing each resistor is the same, and it is equal to the voltage of the battery, which is
[tex]V=120 V[/tex]
So, the voltage in the circuit is 120 V.
3)
The total current in the circuit can be found by using Ohm's law:
[tex]V=RI[/tex]
where
V is the voltage
R is the equivalent resistance of the circuit
I is the current
In this circuit, we have:
V = 120 V
[tex]R=2.73\Omega[/tex]
Re-arranging the equation for I, we find the current:
[tex]I=\frac{V}{R}=\frac{120}{2.73}=44.0 A[/tex]
Learn more about current and potential difference:
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