CIRCUITS

Open Circuit in Series

You already know that a current to pass through a circuit, a closed path is required, so any break in the series circuit causes an open circuit, & stops current flow. There is no power wastage in circuit. If more than 2 lamps are connected in series and if one of them is fused then there is no current flowing through the circuit and so one lamp will light.

Short Circuit in Series

If the short circuit created in series circuit the total resistance will be reduces & a large current will flow through the circuit. Uses of series circuit: 1. Decorative 2. Fan regulator which is connected in series with fan can reduce the speed. 3. To measure circuit current with the help of ammeter. 4. The fuse used for protection of electrical installation. 5. To control the speed of DC Motors. 6. To increase the battery voltages.

Example – 2. A series circuit consist of 3 resistors having values of 20, 30 & 50 ohms respectively. Find the applied voltage, if the current through circuit is 2 ampere? Ans- Given, R1 = 20 ohms, R2 = 30 ohms, R3 = 50 ohms, I = 2A Let us calculate voltage drop across each resistance. Vr1= I x R1 = 2 x 20 = 40 V Vr2= I x R2 = 2 x 30 = 60 V Vr3= I x R3 = 2 x 50 = 100 V therefore, Vr1 = 40 V, Vr2 = 60 V, Vr3 = 100 V Once individual voltage drops are known they can be added to find total or applied voltage. therefore, E1 = Vr1 + Vr2 + Vr3 = 40 + 60+ 100 = 200 V E1 = 200 V …Ans. The total voltage drop across a resistor in a circuit is proportional to the ohmic value of the resistors. Open Circuit in Series You already know that a current to pass through a circuit, a closed path is required, so any break in the series circuit causes an open circuit, & stops current flow. There is no power wastage in circuit. If more than 2 lamps are connected in series and if one of them is fused then there is no current flowing through the circuit and so one lamp will light.

Short Circuit in Series

If the short circuit created in series circuit the total resistance will be reduces & a large current will flow through the circuit. Uses of series circuit: 1. Decorative 2. Fan regulator which is connected in series with fan can reduce the speed. 3. To measure circuit current with the help of ammeter. 4. The fuse used for protection of electrical installation. 5. To control the speed of DC Motors. 6. To increase the battery voltages.

Parallel Circuit

When you connect resistances side by side with the ends connected, they are parallel connected. A parallel circuit is one in which there are one or more points where current divided & flows different paths. When circuit connected in such a way that they provide different current paths it is to be said that connected in parallel. In parallel circuit, total resistance is not the sum of individual resistances. More resistances there are the lower is the total resistance & total resistance is smaller than any of the individual resistance. The total resistance can be find out by a or product over the Sum method to use this method you first multiplied the values of two resistances to get their product then added the values of two resistances to get there sum. Finally you divide the , & the result is total resistance following equation may be used.
This method can be used only for two parallel resistances. This method is not suitable for more than two resistances which are connected in parallel. Combinations of 3 or more unequal resistances in parallel are sometimes used. To find the resistance of such combinations, you first find the total resistance of any two of the resistances. Combine this total in the same way with another of the resistance values & you have total for 3 resistances. Continue to combine the total with additional resistances until all of the resistances has been combine to give the total resistance of all parallel resistances. You can apply another method also, to find out the effective resistance of the parallel circuit. therefore,

The reciprocal of the resistance is known as the conductance of a circuit. Using this term, you can state that the combined conductance of a number of conductors in parallel is equal to sum of their separate conductance. e.g. 1. 4 ohms, 2 ohms & 6 ohms respectively 3 resistors are connected in parallel. Calculate the combined resistance ( Reff.) of the circuit. Ans- Given, R1 = 4 ohms R2 = 2 ohms R3 = 6 ohms

Parallel circuit voltages

In this type of circuit the voltages across each branch resistance is equal to that across the other. In other words, in a parallel circuit, the same voltage is present across the resistors of a parallel group. This voltage is equal to the applied voltage. therefore, VT = Vr1 = Vr2 = Vr3 e.g. 1. 3 resistors of 4ohms, 2 ohms , & 6ohms respectively are connected in parallel. If current flowing through 4 ohms resistance is 2.5 A, current flowing through 2 ohms resistance is 5 A & current flowing through 6 ohms resistance 1.68 A, calculate voltage across each resistance & supply voltage? Ans: Given- R1 = 4 ohms R2 = 2 ohms R3 = 6 ohms Vr1 = I x R1 = 2.5 x 4 = 10 V Vr2 = I x R2 = 5 x 2 = 10 V

Vr3 = I x R3 = 1.68 x 6 = 10 V VT = Vr1 = Vr2 = Vr3 1 = 10 = 10 = 10 = 10V therefore, VT = 10 V

Current in Parallel Circuit:

Current divides among the various branches of a parallel circuit in a manner depending on the resistance of each branch. However source current in a parallel circuit divides among the available paths in relation to the value of resistors in the circuit for a given voltage current varies inversely with resistance.

e.g.1. Three resistances of 10 ohms, 20 ohms & 30 ohms respectively are connected in parallel across 50 volts DC supply calculate the current flowing through each circuit & total current of the circuit?

Ans– Given R1 = 10 ohms R2 = 20 ohms R3 = 30 ohms E = 50 V Ir1 = = = 5 A Ir2 = = = 2.5 A Ir3 = = = 1.67 A R3 30 therefore, Ir1 = 5 A, Ir2 = 2.5 A, Ir3 = 1.67 A Let us calculate circuit current: IrT = Ir1 + Ir2 + Ir3

= 5 + 2.5 + 1.67 IrT = 9.17 A

Short in Parallel Circuit

The equivalent resistance of the straight wire & the resistors, all connected in parallel, will be less than the resistance of the straight wire. This follows from the fact that the total resistance of a parallel circuit is always less than the smallest resistance in the branch. Since a complete path still exists to permit current flow, & the equivalent resistnce is effectively zero, the current will rise rapidly until the current capacity of the fuse is reached. The fuse will then open the circuit causing the current to stop flowing. A short usually causes components to fail in a circuit which is not properly used or otherwise protected. The failure may take the form of burned out resistor, damaged source or a fire in the circuit components & wiring. Uses of parallel circuit 1. In general lighting ( house, shops, offices) 2. Ammeter shunt.

Series – Parallel Circuit

Circuits consisting of three or more resistors may be connected in, partly series, & partly parallel one in which a resistance is connected in series with a parallel combinations & the other in which one or more branches of a parallel circuit consist of resistances in series. While solving circuit first solve parallel circuit first solve parallel circuit & then series circuit by applying parallel circuit & series circuit laws respectively.

 

Electrical Power in Circuits:

Electrical Power, ( P ) in a circuit is the rate at which energy is absorbed or produced within a circuit. A source of energy such as a voltage will produce or deliver power while the connected load absorbs it. Light bulbs and heaters for example, absorb electrical power and convert it into either heat, or light, or both. The higher their value or rating in watts the more electrical power they are likely to consume.

The quantity symbol for power is P and is the product of voltage multiplied by the current with the unit of measurement being the Watt ( W ). Prefixes are used to denote the various multiples or sub-multiples of a watt, such as: milliwatts (mW = 10^-3W) or kilowatts (kW = 10³W).

Then by using Ohm’s law and substituting for the values of V, I and R the formula for electrical power can be found as:

To find the Power (P)

[ P = V x I ]      P (watts) = V (volts) x I (amps)

Also,

[ P = V² ÷ R ]      P (watts) = V² (volts) ÷ R (Ω)

Also,

[ P = I² x R ]      P (watts) = I² (amps) x R (Ω)

So we can see that there are three possible formulas for calculating electrical power in a circuit. If the calculated power is positive, (+P) in value for any formula the component absorbs the power, that is it is consuming or using power. But if the calculated power is negative, (-P) in value the component produces or generates power, in other words it is a source of electrical power such as batteries and generators.

SHORT CIRCUITS:

Definition 

A short circuit is an abnormal connection between two nodes of an electric circuit intended to be at different voltages. This results in an electric current limited only by the Thévenin equivalent resistance of the rest of the network which can cause circuit damage, overheating, fire or explosion. Although usually the result of a fault, there are cases where short circuits are caused intentionally, for example, for the purpose of voltage-sensing crowbar circuit protectors.

In circuit analysis, a short circuit is defined as a connection between two nodes that forces them to be at the same voltage. In an ‘ideal’ short circuit, this means there is no resistance and thus no voltage drop across the connection. In real circuits, the result is a connection with almost no resistance. In such a case, the current is limited only by the resistance of the rest of the circuit.