## Thursday, August 11, 2016

### Resistors in Series and Parallel Problems and Solutions

Resistors in Series

Resistors in series means end to end connection. When they are connected in series, we can find that the current will be the same across all of them and the supplied voltage across them is distributed proportional to the resistance.

We can find the effective resistance of the system when number of resistors are connected in series and also find out the voltage drop across each resistors as shown below. The effective resistance increases in series combination.

This concept is explained here in this video for your reference.

Resistors in parallel

When similar end of all resistors are connected together and the same with the other ends, the connection is called parallel connection. In parallel connection, the voltage across all the elements is same and the current across them is distributed such that it is inversely proportional to resistance.

We can find the effective resistance and the current in each element as shown below. The effective resistance in parallel is less than even the small value of the circuit. The effective resistance decreases in parallel combination.

In a video lesson over you tube parallel resistence resultant is found as shown in the link below.

Variation of resistance Problems and Solutions

We need to find the effective resistance between the two points as shown in the given picture. We can simply solve the problem by bisecting the entire circuit into two identical parts. The two parts are in series with each other and symmetrical. If we are able to find the resistance of one part, by adding the same value to that, we can find the total resistance of the system given.

As we have bisected the resistor into two parts, its length so its resistance also becomes half. By identifying the resistors in series and parallel and measuring their effective resistance, we can find the total resistance of the circuit as shown below.

Problem and Solution

This problem is about percentage change in the resistance of a wire when there is a change in its length alone. No information is given in the problem about its area. As the volume of the wire remains constant, we need to write area in terms of length and volume. Thus we can prove that resistance is directly proportional to the square of the length of the wire.

The problem is solved as shown below.

Problem and solution

This problem is about variation of resistance with mass of the wire. There is information in the problem about its length but not about area. We can change the area interms of mass and solve the problem as shown in the diagram below.

Problem and solution

This problem is about current passing in a wire when multiple wires are connected in parallel. The total current across the combination is given to us and resistance of each wire is given. We know that if resistors are connected in parallel, the voltage across them is same. Hence the current flow is reciprocal to resistance and the problem can be solved as shown below.

Problem and solution

This problem is about finding a voltage across a resistor when multiple resistors are connected in the circuit as shown in the diagram.

By identifying the elements and currents across them, we can solve the problem as shown below.

Problem and solution

If two parts of a circle separated by an angle are two wires having different resistance, we need to measure the effective resistance of the circuit. The problem is solved as shown below.

Problem and solution

This problem is about to find the effective resistance of the system where infinite resistors are connected as shown in the diagram. We can identify the symmetry in the ladder and we can say that the circuit is the combination of similar symmetrical parts. Except one part, we can assume that all other parts together are having some resistance and even with the other remaining ladder, the answer still remains same. Simply because of infinite ladders, adding or removing one ladder is not going to make a big difference to the entire system significantly.

Thus we can solve the problem as shown below.

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