Why Is the Voltage in Parallel Resistors the Same? Answered

Parallel circuits are used in many devices that we use every day because they have many advantages over series ones. One of these advantages is the same voltage across any resistor in the circuit. So, why is voltage in parallel resistors the same?

Why Is the Voltage in Parallel Resistors the Same?

Because any parallel resistors are connected to the same wire nodes, the wires connecting them start at the same point and then end at the same point. If two resistors seem to be connected in parallel and even have the same voltage, but they start and end at different points, they are not parallel.

The voltage or the potential difference is the difference in voltage between two points in an electric circuit; if the points are the same for any number of resistors between them, then the voltage will be the same because the difference is the same.

Why Is the Voltage in Series Resistors Not the Same?

Because the series resistors are not connected to the same wire nodes, the wires connecting the resistors start and end at different points. When a resistor is connected in series with another resistor, the first resistor is connected from one side directly to the voltage source first pole, such as batteries.

Meanwhile, the second side is connected to the next resistor, the second resistor is connected from one side to the first resistor, and its second side is connected to the other pole for the voltage source. As a result, the two resistors are connected to two different points; therefore, they have different voltages.

Why Is the Current in Parallel Resistors Not the Same?

Because the current, when it enters a parallel connection, divides into two smaller currents, the value of each current depends on the value of the resistor it’s passing through. Therefore, the only case where the parallel resistors can have the same current is when the two resistors have the same resistance.

For example, when two resistors are connected in parallel with the same resistance 2 Ω, the current entering them will be divided by two, so if the current is 4 amperes, each resistor will have 2 amperes passing through it. The voltage across each resistor always stays the same regardless of their resistance.

Why Is the Current in Series Resistors the Same?

Because the current entering the first resistor is the same one entering the next resistor, each resistor is connected to the previous resistor before it. As a result, the current doesn’t pass through any junctions or branches; therefore, it doesn’t divide or lose any amperes between the resistors.

For example, when some resistors are connected in series regardless of their resistance, the current passing through the first resistor will be the same until the last resistor that is connected in series, which means that if the current is 4 amperes will stay at 4 amperes in each resistor in the circuit.

Related Readings:

Why Is Voltage Constant in Parallel Circuit but Not…

Why Do Parallel Resistors Have Less Resistance?

What Color Wires Can Go Together? Complete Guide

What Happens if You Switch Neutral And Ground Wires?

How To Measure and Identify Resistor Using…

How to Identify Line and Load Wires? – 4 Ways

Why Do Parallel Resistors Have Less Resistance?

The parallel resistors have less resistance due to their way of connection; the resistors in parallel are connected in more than one branch, which results in a total resistance less than the one of the same resistors if they were connected in parallel. The series connections always have more resistance.

This can be seen in the formula of the total resistance in parallel connections, where the resistance of each resistor is multiplied by the others. Then, the result is divided by their summation, which results in a total resistance smaller than the smallest resistor in the circuit.

  • R_{eq}=\frac{R_{1}R_{2}R_{3}}{R_{1}R_{2}+R_{2}R_{3}+R_{1}R_{3}}

Meanwhile, in the series connection, the total resistance results from the summation of the resistance of each resistor; this results in a total resistance bigger than the biggest resistor in the circuit.

  • R_{eq}=R_{1} + R_{2} + R_{3} + ...

Is the Parallel Connection Better Than the Series Connection?

Yes, the parallel connection is better than the series in many cases because the total resistance in the series is always bigger than the parallel, which gives the parallel connections a big advantage over the series ones. Parallel connections have other advantages as well, for example:

Advantages of Parallel Connections

  • Same Voltage Across Resistors
    In the parallel connections, the voltage across each resistor is the same; this can be used in many applications; for example, in lightning systems in houses, the lamps in households are connected parallelly, therefore having the same potential difference, which means the same brightness in all light bulbs.
  • Different Branches For Devices
    The devices in parallel connections are connected in different branches, which protects the other devices from failing if one device fails; this also can be useful when turning any device or appliance, so the other devices continue to work finely.

Disadvantages of Series Connections

  • Different Voltage Across Resistors
    In the series connections, the voltage across each resistor is different from the others, which makes it impossible to use series connections in many applications; for example, the lamps in households can’t be connected in series because this would affect the brightness of the bulbs with the increase of bulbs connected.
  • Same Branch For Different Devices
    The devices in series connections are connected on the same branch, which makes the circuit open in case of any device is turned off or fails.

How to Calculate Total Resistance in Parallel Resistor?

  1. Understand your circuit. Any parallel circuit consists of many branches; they all start at the same point and then reconnect at one point. The current is divided between the branches depending on the value of each resistor in the parallel connection. The smallest resistor has the largest current.
  2. Calculate the resistance of each branch. The current passes through each resistor, which affects the current in a small effect, but you have to sum all these effects of the resistors to get the total resistance. So, you start with R= V/I to get the resistance of each resistor; then you get the total resistance by Req = 1/R1 + 1/R2 + 1/R3 +…
  3. Don’t miss branches with zero ohms. If a branch has no resistance or zero ohms, the current will leave any parallel resistor to it and only flow through the branch with zero resistance. Branches of no resistance can happen if they have no resistors or their resistors have failed.

Source

What Are The Applications of Parallel Circuits?

  • Houses
    It’s nearly impossible that a house doesn’t use parallel circuits in its wiring because the parallel connections allow you to cut off the power from one device or appliance without cutting off the other devices. In addition, parallel circuits protect the devices against the short circuits because each device has access to the same power.
  • Infrastructure
    Parallel circuits are one of the main components used in building infrastructure and providing power to big populations. Engineers have used parallel circuits to create more efficient and secure power grids, and these grids continue to work properly even if one circuit goes down.
  • Devices
    Many devices and electrical appliances use parallel circuits because these devices get benefit from more than one power source in the parallel connections, for example, using more than one battery in portable devices. Parallel circuits are the main reason behind Christmas lights; imagine one bulb fails and the others follow her.

Conclusion

To sum up, voltage is the same in parallel circuits or resistors because the resistors are connected to the same wire nodes. The resistors start at the same node and reconnect at the same node; this makes the resistors connected directly to the power or voltage source, therefore the same voltage across the whole circuit.

Meanwhile, the resistors are not connected to the same wire nodes in the series circuits. The resistors could be connected from one side to the voltage source and connected from the other side to another resistor, or they could be connected from both sides to resistors. Therefore, the voltage across the circuit is different.

Parallel circuits are more useful and more used than the series ones; the parallel circuits have many advantages over the series ones. One of the big advantages of parallel circuits is that they have the same potential difference across each resistor; you can see this, especially in lightning systems where all bulbs have the same brightness.

Scroll to Top