The relationship between total resistance and partial resistance in parallel circuits. The current distribution rules of parallel circuits.
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The relationship between total resistance and partial resistance in parallel circuits. The current distribution rules of parallel circuits.

Posted Date: 2024-01-23

In a parallel circuit, the voltages at both ends of each branch of the parallel circuit are equal. U=U1=U2 (not exactly equal everywhere). In addition, the current in the main circuit of a parallel circuit is equal to the sum of the currents in each branch. In a series circuit, the current is equal everywhere. (This is not a parallel circuit.) In a series circuit, the voltage across all appliances is equal.

one. Literally speaking, parallel connection means parallel connection. There are more than two resistors with one end connected together and the other end connected together. These two nodes are externally applied voltages, forming a circuit that branches again. This is called a parallel circuit. The two light bulbs in the picture above are connected in parallel, and of course, the two switches that control the light bulbs are also connected in parallel.

The relationship between total resistance and partial resistance in parallel circuit

In a parallel circuit, there is a specific relationship between the total resistance and the partial resistance. The total resistance refers to the total impedance of the entire parallel circuit, while the partial resistance refers to the impedance of each branch resistor.

In a parallel circuit, the individual branches are independent and they are connected simultaneously to the same supply voltage. Therefore, when current enters a parallel circuit, it is divided among the branches, passing through the resistance of each branch.

The total resistance (RT) is equal to the reciprocal of the sum of the reciprocals of the individual branch resistances (R1, R2, R3,...). The expression formula is as follows:

1/RT = 1/R1 + 1/R2 + 1/R3 + 。..

Right now:

RT = 1 / (1/R1 + 1/R2 + 1/R3 + 。..)

It can be seen that when the branch resistances in a parallel circuit are equal, the total resistance is equal to the average of the reciprocals of the sum of the reciprocals of the individual branch resistances. In other words, when the branch resistances are equal, the total resistance decreases.

In addition, the total current (IT) is equal to the sum of the individual branch currents (I1, I2, I3,...):

IT = I1 + I2 + I3 + 。..

The total current is equal to the algebraic sum of the individual branch currents.

For a parallel circuit, the total resistance is the reciprocal of the sum of the reciprocals of the partial resistances, and the total current is equal to the sum of the individual branch currents. When the branch resistances are equal, the total resistance decreases and the total current is equal to the algebraic sum of the individual branch currents. These relationships are very useful in analyzing and calculating the characteristics and behavior of parallel circuits.

Voltage relationships in parallel circuits

In a parallel circuit, the relationship of voltages can be described by the following points:

1. The total voltage is equal to the equality of the individual branch voltages: In a parallel circuit, each branch is connected to the same supply voltage. Therefore, the voltage of each branch is equal to the supply voltage.

2. Independent branch voltages: In a parallel circuit, each branch is independent and has the same power supply voltage. This means that regardless of the size of the resistors in the branches, their voltage remains the same.

3. The current in a branch with resistance is inversely proportional to the voltage: According to Ohm's law, I (current) = V (voltage) / R (resistance). Since branch voltages are equal in a parallel circuit, the branch with smaller resistance will carry a larger current and the branch with a larger resistance will carry a smaller current.

4. Equivalent resistance and current division: In a parallel circuit, if the supply voltage and the resistance value of each branch are known, the current in each branch can be calculated using Ohm's law. These branch currents can then be added to obtain the total current. Another method is to calculate the equivalent resistance of the parallel branches and divide the total voltage by the equivalent resistance to calculate the total current.

Parallel circuit current distribution rules

In a parallel circuit, the current is distributed according to a certain rule, which is called the current distribution rule of the parallel circuit. The following are several key points of the current distribution rules of parallel circuits:

1. The sum of the currents of each branch is equal to the total current: In a parallel circuit, the total current is equal to the sum of the currents of each branch. This means that regardless of the magnitude of the resistance in the branches, their respective currents add up to the total current.

2. Branch currents are independent: In a parallel circuit, each branch is independent and their currents are independent of each other. The magnitude of the branch current is not affected by the currents of other branches. Each branch determines the magnitude of the current based on its own resistance and Ohm's law.

3. Current distribution is inversely proportional to resistance: According to Ohm's law, current (I) is equal to voltage (V) divided by resistance (R). Since the voltages are equal in a parallel circuit, the branch currents are inversely proportional to their corresponding resistances. The branch with smaller resistance will distribute larger current, and the branch with larger resistance will distribute smaller current.

4. Current distribution law: According to the current distribution law, the current of each branch is proportional to the reciprocal of its resistance. The expression is I = V/R, where I is the branch current, V is the supply voltage, and R is the branch resistance. By adjusting the size of the branch resistors, the distribution of current in the parallel circuit can be controlled.

The distribution of branch currents depends on Ohm's law and current distribution laws, and these laws apply to linear resistors. In some special cases, such as the presence of non-linear components such as diodes or capacitors, the current distribution may be affected. Therefore, for complex parallel circuits, additional factors and nonlinear characteristics need to be considered.


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