Voltage Across Resistors In Parallel

In summary, the conversation discusses a circuit with a 31.0 Ω resistor and the calculation of current and potential difference in the circuit. The voltage drop is found to be the same across two resistors in parallel due to the definition that they are connected between the same two nodes. This is compared to two climbers reaching the same point on a mountain despite taking different routes.
  • #1
Bashyboy
1,421
5

Homework Statement


Consider the circuit shown in the figure below. (R = 31.0 Ω.)

(a) Find the current in the 31.0 Ω resistor.

(b) Find the potential difference between points a and b.


Homework Equations





The Attempt at a Solution



I am reading the solution of this problem given by the author, and for the most part I understand it, except for this one critical part:

"In diagram (iii), the current above goes through the equivalent resistor [itex]R_{iii}[/itex] to give a voltage drop across this resistor of [itex]ΔV = IR_{iii}[/itex]. n diagram (ii), we see that this voltage drop is [itex]ΔV_{ab}[/itex] and is the same across the 10.0-Ω resistor and the 5.00-Ω resistor."

Why is the voltage drop the same across the two resistors in parallel?
 

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  • #2
Why is the voltage drop the same across the two resistors in parallel?

By definition two resistors in parallel are both connected to the same nodes. In capture.jpg these nodes are a and b.

If you connect two resistors in parallel to an ideal 9V battery they will both have 9V across them.
 
  • #3
So, it simply follows from definition, and there isn't any other reason?
 
  • #4
No you missunderstood what I said. The definition of parallel is that the resistors are connected between the same two nodes. They have the same voltage drop because they are both connected to the same nodes.

Imagine two climbers go up a mountain. They start at the same point at the bottom and reach the same point at top. They might take different routes but both will measure the same change in altitude because they started and finished at the same places.
 
  • #5


I would approach this question by first understanding the concept of parallel resistors. In a parallel circuit, the voltage across each resistor is the same, as they are connected to the same two points in the circuit. This can be explained by Ohm's Law, which states that voltage is equal to current multiplied by resistance (V=IR). Since the current is the same throughout the circuit, the voltage drop across each resistor will be proportional to its resistance. In other words, the higher the resistance, the larger the voltage drop. Therefore, in this circuit, the voltage drop across the 10.0-Ω resistor and the 5.00-Ω resistor will be the same, since they have the same current flowing through them. This concept can also be visualized using Kirchhoff's Voltage Law, which states that the sum of all voltage drops in a closed loop must equal the sum of all voltage sources. In this circuit, the voltage drop across the 31.0 Ω resistor (ΔV=IR) must equal the voltage drop across the parallel combination of the 10.0-Ω and 5.00-Ω resistors. Therefore, the voltage drop across the two parallel resistors must be the same.
 

What is the definition of voltage?

Voltage is a measure of the electric potential difference between two points in an electrical circuit. It is measured in volts (V) and represents the amount of energy needed to move a unit of charge from one point to another.

How is voltage distributed in a parallel circuit?

In a parallel circuit, the voltage is the same across each branch or resistor. This means that the total voltage of the circuit is equal to the voltage across each individual resistor.

What happens to voltage when resistors are added in parallel?

When resistors are added in parallel, the total resistance of the circuit decreases. This leads to an increase in current, which causes the voltage across each resistor to remain the same.

How do you calculate the total voltage in a parallel circuit?

The total voltage in a parallel circuit is equal to the voltage across any one of the resistors. This can be calculated using Ohm's law, where V (voltage) = IR (current x resistance).

What is the purpose of using resistors in parallel?

Using resistors in parallel allows for more current to flow through the circuit, as the total resistance is lower. This can be useful for distributing power evenly or for creating complex circuits with multiple branches.

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