# Relationship of current and voltage resistors connected in series parallel circuit

### What is a Series-Parallel Circuit? | Series-parallel Combination Circuits | Electronics Textbook Jul 10, A series circuit is a circuit in which resistors are arranged in a chain, which the resistors are arranged with their heads connected together, and their tails connected together. The current in a parallel circuit breaks up, with some flowing along each The voltage across each resistor in parallel is the same. Practical circuits often contain very complicated combinations of resistors. It is, therefore, useful to of two simple rules. These rules relate to resistors connected in series and in parallel. It is clear that the same current \$I\$ flows through both. A parallel circuit is one that has two or more paths for the electricity to flow, the loads are of a Parallel Circuit is NOT equal to the sum of the resistors (like in a series circuit). As you add more and more branches to the circuit the total current will increase Voltage is the same across each component of the parallel circuit.

Chapter 7 - Series-parallel Combination Circuits With simple series circuitsall components are connected end-to-end to form only one path for electrons to flow through the circuit: With simple parallel circuitsall components are connected between the same two sets of electrically common points, creating multiple paths for electrons to flow from one end of the battery to the other: With each of these two basic circuit configurations, we have specific sets of rules describing voltage, current, and resistance relationships. Voltage drops add to equal total voltage. All components share the same equal current. Resistances add to equal total resistance. All components share the same equal voltage.

### Series and Parallel Circuits

Branch currents add to equal total current. Resistances diminish to equal total resistance. Instead, we will have to identify which parts of that circuit are series and which parts are parallel, then selectively apply series and parallel rules as necessary to determine what is happening.

Throughout this unit, there has been an extensive reliance upon the analogy between charge flow and water flow. Once more, we will return to the analogy to illustrate how the sum of the current values in the branches is equal to the amount outside of the branches. The flow of charge in wires is analogous to the flow of water in pipes. Consider the diagrams below in which the flow of water in pipes becomes divided into separate branches.

At each node branching locationthe water takes two or more separate pathways. The rate at which water flows into the node measured in gallons per minute will be equal to the sum of the flow rates in the individual branches beyond the node. Similarly, when two or more branches feed into a node, the rate at which water flows out of the node will be equal to the sum of the flow rates in the individual branches that feed into the node.

The same principle of flow division applies to electric circuits. The rate at which charge flows into a node is equal to the sum of the flow rates in the individual branches beyond the node. This is illustrated in the examples shown below. In the examples a new circuit symbol is introduced - the letter A enclosed within a circle. This is the symbol for an ammeter - a device used to measure the current at a specific point. An ammeter is capable of measuring the current while offering negligible resistance to the flow of charge.

Diagram A displays two resistors in parallel with nodes at point A and point B.

How To Solve Any Resistors In Series and Parallel Combination Circuit Problems in Physics

Charge flows into point A at a rate of 6 amps and divides into two pathways - one through resistor 1 and the other through resistor 2.

The current in the branch with resistor 1 is 2 amps and the current in the branch with resistor 2 is 4 amps. After these two branches meet again at point B to form a single line, the current again becomes 6 amps. Thus we see the principle that the current outside the branches is equal to the sum of the current in the individual branches holds true. Four nodes are identified on the diagram and labeled A, B, C and D. Charge flows into point A at a rate of 12 amps and divides into two pathways - one passing through resistor 1 and the other heading towards point B and resistors 2 and 3.

The 12 amps of current is divided into a 2 amp pathway through resistor 1 and a 10 amp pathway heading toward point B. At point B, there is further division of the flow into two pathways - one through resistor 2 and the other through resistor 3. The current of 10 amps approaching point B is divided into a 6-amp pathway through resistor 2 and a 4-amp pathway through resistor 3.

## Parallel Circuits

Thus, it is seen that the current values in the three branches are 2 amps, 6 amps and 4 amps and that the sum of the current values in the individual branches is equal to the current outside the branches. Equivalent Resistance The actual amount of current always varies inversely with the amount of overall resistance. There is a clear relationship between the resistance of the individual resistors and the overall resistance of the collection of resistors.

Since the circuit offers two equal pathways for charge flow, only one-half the charge will choose to pass through a given branch. With three equal pathways for charge to flow through the external circuit, only one-third the charge will choose to pass through a given branch.