 Hello and welcome to the session. In this session we will discuss switching circuits. First of all let's see what is a switch? A switch is a device which is attached to a point in an electric current. A switch can have two positions. It can be either closed or open. That is we can have two switches, a closed switch or an open switch. This is a closed switch and this is an open switch. This closed switch permits the flow of current. This open switch prevents the flow of current. A closed switch means that the switch is on and an open switch means that the switch is off. So we can say that a switching circuit is a connection, number of switches and so on in which the electric current may or may not flow for a given situation switches. Now if we write here P which is a switch then we say that the switch P is closed and if we write here P then we say that the switch P is open. Now in case of the closed switch P that P is and in case of the open switch P we say that the P is false. To every switch on a circuit we attach two values. Now if a switch is closed then we give it a value 1 and if the switch is open we give it a value 0. So as in this case P is closed so P would be 1 and here P is open so P would be 0. Now the switches can be in series in this case the switches P and Q are in series and this resulting circuit is denoted by P into Q or P consumption Q. In this case the current flows from 2Y if both the switches P and Q are closed that is if P consumption Q is through. In this case only the current will flow and if either of the two switches are open like if P is open and Q is closed then the current will not flow or if Q is open and P is closed then also the current will not flow. Current will flow only when P and Q are both closed. Now in this case the switches P and Q are in parallel when the switches P and Q or say any two switches are connected in parallel then this corresponding circuit so obtained is denoted by P plus Q or P distribution Q. And in this case the current flows from if either P or Q or both that is if P distribution Q is true. P is closed and Q is open then the current will flow if P is open Q is closed then also the current will flow and if both P and Q are closed then the current will flow. This is how we can represent a network of switches in parallel or in series. Consider this network of three switches P Q and R where you can see that the switches P and Q are in series and R is parallel to these two switches as we know in series the current would flow only when both the switches are closed. So P and Q should be closed parallel to this series of P and Q then the current will flow when both the switches P and Q are closed or R is closed. That is the current will flow when P conjunction Q the whole disjunction R is true. In this case the current flows. On its discuss the AND switching circuit or P Q circuit as we have denoted the symbol 1 for the closed switch and symbol 0 for the open switch likewise we have the symbol 1 to denote that the lamp lights and symbol 0 to denote that the lamp does not light. Now if we have P and Q two switches in a circuit and when P is on then Q is off then this means 2 is the complement of P and it is denoted as P complement. Also when P is off then Q is on also means that Q is the complement of P and if the two switches are simultaneously on or simultaneously off then we would denote them by the same letter. Now if the switch is open then it is denoted by a symbol 0 then in that case the current will not flow and so the lamp would not light and so the state of lamp also in that case would be 0 that is it won't light up. And if the switch is closed which is denoted by the symbol 1 then in that case the current would flow and so the lamp would light and so the state of lamp would also be denoted by 1. Now we will consider two switches P and Q in series raised to the part 2 that is instead of two switches so we have 2 raised to the part 2 that is 4 possible in the circuit in which the two switches P and Q are in series. So this is the first case in which we have the two switches P and Q in series and as you can see both the switches P and Q are open P is open Q is also open in this case this B is the battery and L is the lamp in this circuit. This is the second state in which the switch P is open and the switch Q is closed. This is the third state in which the switch P is closed and the switch Q is open. This is the fourth state in which both the switches P and Q are closed. Now in the first condition both the switches P and Q are open so this means state of the switch P would be 0, state of switch Q would be 0 as they are open and since they are open so no current would flow and thus the state of lamp L would be 0 that is the lamp would not light. In the second state we have the switch P is open and the switch Q is closed so P is open and Q is closed and so the current would not flow as when two switches are in series then the current would flow only when both the switches are closed. So in this case also the current would not flow and the lamp would not light and so here we have 0. In this third state we have P is closed Q is open so again the current would not flow and so the lamp would not light so here we have 0. Now in the fourth state we have that P is closed and also the switch Q is closed which means that the current would flow and so the lamp would light. Now this circuit in which the two switches P and Q are in series is called the AND circuit or PQ circuit because in this case the lamp lights only when both the switches P and Q are closed. We can have more than two switches in a series like if we have three switches in series then there would be two rays to the power 3 that is eight possibilities which could be shown in the same way as we have done for the two switches in series. So this completes the session hope you have understood the concept of the switching circuits and the PQ or AND circuit.