(Ii) Potential Will Be Contributed by Both Charges

TMA 03

Q2. (a) )(i) We will determine the potential energy between two charges at r = 2.4*10^-4m and when r = 2*2.4*10^-4m.The difference between these two energies will be the energy needed to double the separation.

Hence, energy needed to double separation = 5.76-2.88= 2.88 J

Here charges are of opposite nature, there will be attractive force between them. Hence, energy will be consumed in doubling the separation.

(ii) Potential will be contributed by both charges.

Hence, net potential

(b) (i) Electric field = 100N/C = 100V/m

Distance between plates = 10mm = 10*10^-3m

Voltage between plates = 100*10*10^-3 = 1V

(ii) Charge on proton = 1.6*10^-19C

Potential = 1V

Hence, change in energy = charge*potential

= 1.6*10^-19*1

= 1.6*10^-19J

(iii)Equi-potential lines will be parallel to the plates as shown below.

(iv) Initially, there is no charge on the plates. Let us suppose that some charge is brought to the plates and this charge spreads over the plates. Opposite charge is induced on the other plate. Let us bring come more charge on the plate. As this charge is of the same nature as the earlier charge, there will be repulsion and some work will have to be done to bring this charge to the plate. Hence, there will be some energy stored in the system. The more the charge is brought to the system, the more is the energy stored in the system. This is how energy is stored in a capacitor.

Q3.(a)

KIRCHOFF’S LAWS

These laws are very much useful for circuit problems. There are two Kirchhoff’s laws. One Kirchhoff’s voltage law and the other one is Kirchhoff’s current law.

According to Kirchhoff’s voltage law, algebraic sum of voltage in any loop is zero. If we consider voltage rise as positive and voltage drop as negative, we will have voltage rise as equal to voltage fall.

According to Kirchhoff’s current law, algebraic sum of currents at any node in any electric circuit is always zero. Alternatively, we can say that sum of incoming current is always equal to the sum of outgoing currents.

Using these laws, we can find currents flowing in circuit components.

OHM’S LAW

According to this law, voltage across in any resistance is proportional to the current flowing through the resistance. It must be ensured that the resistance does not change due to change in physical conditions such as temperature etc. when the current and voltage across the resistance are being measured.

(b)(i) Let V be the battery voltage. This voltage is applied across 1m long wire. Voltage will drop across this wire at the rate of V/1 = V volts per meter.

Voltage drop across AC =

As voltmeter reading is zero, voltage drop across PRT will be equal to the voltage drop across wire AC. Current I flowing through PRT and resistance R will be given by

where R1 = PRT resistance

Hence, voltage drop across PRT =

Applying KVL across ACDA, we get = …. (1)

Similarly voltage drop across wire CB =

Voltage drop across R =

Applying KVL across CBDC, we get = …. (2)

Dividing (1) by (2), we get

R = 224 ohms, l=1m l1 = 0.44m; hence, R1=

(ii) Length L = 9m = 900cms, dia = 8*10^-2mm = 8*10^-3cms, ρ = resistivity =? Hence,

(c) The wire should be as uniform as possible. If this is not so, the wire resistance will not be uniform and, hence, voltage drop per unit length will not be same. This will affect the final result/measurements.

Temperature should remain same throughout the experiment. If temperature is not remaining same, there will be change in the resistance values and it will change the voltage per unit length. While determining the unknown value, we assume that the voltage drop per unit length is same. If voltage drop per unit length changes, the very assumption for making calculations will be violated and our results will be wrong. Hence, maintaining same temperature is must for correctness of the final results.

As current passes through the wire, there will be some heat developed leading to temperature rise and changing the resistance. It is inevitable but we can make the measurements as fast as possible to reduce the effect of heat generated in the wire. Hence, measurements should made as fast as possible.