IEMDaily - Video Lecture Notes

Definition

Energy conservation in a circuit

In an electrical circuit, total power supplied equals the total power delivered at all instants.
Consider a circuit consisting of an ideal voltage source with emf

ε

and a resistance

R

.
Power in the emf source is

P_{s} = - V I

Power in the resistance is

P_{r}

By ohm's law,

V = I R

⟹ P_{r} = V I

∴ P_{s} + P_{r} = 0

Definition

Ammeter and Voltmeter

Ammeter is a device used to measure the current in a circuit. It is connected in series to the element through which the current flows. Resistance of an ideal ammeter is zero. Sometimes a resistance is connected in parallel to the ammeter to increase the range of an ammeter.
Voltmeter is a device used to measure the potential difference in the circuit. It is connected in parallel to the element through which potential drop is to be measured. Resistance of an ideal voltmeter is infinite.

Definition

Construction of Water Voltameter

The water voltameter is shown in fig.
It consists of a glass vessel, having base of wood or ebonite.
Two platinum electrodes are fused at the base.
The vessel is filled with water to which a few drops of sulphuric acid are added to make it conducting, as the pure water is a bad conductor of electricity.
2 long test-tubes filled with acidic water are inverted over each electrode.

Definition

Working of Water Voltameter

When a battery is connected between the electrodes and current is passed, then the water is decomposed and oxygen and hydrogen gases are connected over anode and cathode.
The ratio of oxygen and hydrogen thus found is 1:2. The following reaction takes place.
When a battery is connected between the electrodes and current is passed,

H_{2} S O_{4} \to 2 H^{+} + S O_{4}^{-}

The positive hydrogen ion move towards cathode and take electron from cathode and hence hydrogen gas is formed, which is collected over the cathode in an invert test tube.

2 H^{+} + 2 e^{-} \to 2 H

2 H \to H_{2}

The negatively charge sulphate ions move towards the anode and give the lectrons to the anode and cahnge into sulphate radical. The sulphate radical reacts with water and gives sulphurics acid and oxygen gas is formed. The oxygen gas thus formed is collected over the anode in inverted tube

S O^{{- -}_{4}} \to S O_{4} + 2 e^{-}

2 H_{2} O + 2 S O_{4} \to 2 H_{2} S O_{4} + O_{2}

Definition

working of Copper voltameter

When the copper sulphate is dissolved into water it is dissociated into

C u^{2 +}

and

S O_{4}^{2 -}

C u S O_{4} \to C u^{2} + S O_{4}^{2 -}

When current is made to flow through the electrolyte solution with the help of bttery potential difference is applied between the electrodes, then positive ions

C u^{2 +}

moves towards cathode and

S O_{4}^{2 -}

ions moves towards anode.

C u^{2} + 2 e^{-} \to C u

Sulphate ions are negatively charged and moves towards the anode, they give electrons to anode and becomes electrically neutral. This sulphate radical reacts with Cu metal of electrode and gives

C u S O - 4

S O_{4}^{2 -} \to S O_{4} + 2 e^{-}

C u + S O_{4} \to C u S O_{4}

Definition

Construction of Copper Voltameter

A copper voltameter consisits of a glass vessel containing copper sulphate solution and 2 copper electrodes partially dipped into the solution. The lectrode are connected with battery as shown in Fig.
When a steady current is made to pass through the

C U S O_{4}

solution, then the copper is deposited on the cathode and an equal amount of copper is lost by the anode and this amount gets dissociated into the solution.
The concentration of copper sulphate solution remains unchanged during the electrolysis.

Definition

Working of Silver Voltameter

When a battery is connected across the elctrodes the

A g^{+}

ions move towards cathode, and take electrons from the cathode and become neutral, and are deposited on it.
At Cathode :

A g^{+} + e^{-} \to A g

At Anode :

N O_{3}^{-} - e^{-} \to N O_{3}

Definition

Construction of Silver Voltameter

It consists of platinum bowl, with a solution of

A g N O_{3}

. Platinum bowl acts as cathode. A pure silver plate is immersed into silver nitrate which serves as anode.

Definition

Galvanometer as an ammeter

For measuring currents, the galvanometer has to be connected in series, and as it has a large resistance, this will change the value of the current in the circuit. To overcome these difficulties, one attaches a small resistance

r_{s}

,called shunt resistance, in parallel with the galvanometer coil; so that most of the current passes through the shunt. The resistance of this arrangement is,

R_{G} r_{s} / (R_{G} + r_{s}) ≃ r_{s}

(i f R_{G} >> r_{s})

Definition

Shunt

In an ammeter, a resistor having a small resistance is connected in parallel with the coil. This resistor is called shunt. It allows electric current to pass around another point in the circuit by creating a low resistance path.

Definition

Galvanometer as an ammeter

Since Galvanometer is a very sensitive instrument therefore it can't measure heavy currents. In order to convert a Galvanometer into an Ammeter, a very low resistance known as "shunt" resistance is connected in parallel to Galvanometer. Value of shunt is so adjusted that most of the current passes through the shunt.In this way a galvanometer is converted into ammeter and can measure heavy currents without fully deflected.