DC CIRCUITS SLIDES BY ZIL E HUMA

OBJECTIVES MULTILOOP CIRCUITS JUNCTION BRANCH KIRCHHOFF’S FIRST RULE MEASURING INSTRUMENTS – THE AMMETER – THE VOLTMETER – THE POTENTIOMETER

MULTILOOP CIRCUITS The circuit given below is containing more than one loop. We have neglected the internal resistance of the batteries here. 11 22 i3 i2i1 R3 R2R1 d cba

Junction: Junction: – A junction in a multiloop circuit is a point in the circuit at which three or more wire segments meet. Branch: Branch: – A branch is any circuit path that starts on one junction and proceeds along the circuit to the next junction.

There are two junctions in the circuit, at b and d. There are three branches in the circuit, that is there are three paths that connect junctions b and d. – bad – bcd – bd

Each branch has its own individual current. The three unknown currents are labeled i 1, i 2, i 3. The direction of the currents have been chosen arbitrarily. Equating the current entering and leaving the junction, we obtain – i 1 + i 3 = i

The above equation suggests a general principle for the solution of the multiloop circuits – At any junction the sum of currents leaving the junction (those with arrows pointing away from the junction) equals the sum of the currents entering the junction(those with arrows pointing towards the junction). This is the junction rule, also known as kirchhoff’s first rule.

Our basic rules for analyzing circuits are 1- the conservation of energy (the loop rule) 2- the conservation of charge (the junction rule)

In multiloop circuits there is more than one loop and the current in general is not the same in all parts of any given loop. If we traverse the left loop in the counter clock wise direction starting and ending at b. The loop rule gives  1- i 1 R 1 + i 3 R 3 = 0

The right loop gives (counter clockwise) - i 3 R 3 - i 2 R 2 -  2 = 0

MEASURING INSTRUMENTS THE AMMETER – An instrument used to measure currents is called an ammeter. – To measure the current in a wire, you usually have to break or cut the wire and insert the ammeter so that the current to be measured passes through the meter. – It is essential that the resistance Ra of the ammeter be very small compared to other resistances in the circuit.

THE VOLTMETER – A meter to measure potential difference is called a voltmeter. – To find the potential difference between any two points in the circuit, the voltmeter terminals are connected at those points, without breaking the circuit. – It is essential that the resistance R of a voltmeter be very large compared to any circuit element across which the voltmeter is connected.

THE POTENTIOMETER – A potentiometer is a device for measuring an unknown emf  x by comparing it with a known standard emf.