(i) If S is in position A, the resistance 20 Ω short-circuited.
\(\therefore I_{g}=\frac{1.5}{20+10}=0.05 \mathrm{~A}\)
(ii) If S is in position B, circuit will be as shown in the 
Now, \( I=\frac{1.5}{20+10+20 \| 20} \)
\(I=\frac{1.5}{20+10+10}=\frac{1.5}{40} \mathrm{~A} \)
∴ Reading of galvanometer \(=\frac{I}{2}=0.01875 \mathrm{~A}\)

(a) X = 8.2\(\Omega\)
(b) 60.5 cm from A
(c) No deflection

\( I=n_e A v_x=n_y e A v_y \\ \Rightarrow \ \frac{v_X}{v_Y}=\frac{n_Y}{n_X}=\frac{n_Y}{2 n_Y}=\frac{1}{2} \)

Applying Kirchhoff's loop rule for loop ABEFA
6 + 3 + R₁ \(\times\) 0 - 3I₁ + 1 - 2I₁ = 0
or  10 - 5I₁ = 0
or I₁ = 2A
For loop BCDEB,
4 - I₁ . R + R₁  \(\times\) 0 - 3 = 0
or  1 - 2R = 0
\(\therefore \quad R=\frac{1}{2} \Omega\)

Potential difference between A and D through path
ABCD is 6 + 4 - I₁ R = V_AD \(\Rightarrow \quad 10-2 \times \frac{1}{2}=V_{A D}\)
\(\therefore\) V_AD = 9 V

Since, the positive terminal of the batteries are connected together, so the equivalent emf of the batteries is given by E = 200 - 10 = 190 V
Hence, the current in the circuit is given \(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

(i) DE is the region of negative resistance because the slope of curve in this part is negative.
(ii) BC is the region where Ohm's law is obeyed because in this part, the current varies linearly with the voltage.

P = I²R  or  log P = 2 log I + log R;
Differentiating it, we get
\(\frac{\Delta P}{P}=\frac{2 \Delta I}{I}+0\)
% change in power 
\( =\frac{\Delta P}{P} \times 100=\frac{2 \Delta I}{I} \times 100 \\ =2 \frac{1}{100} \times 100=2 \% \)

Energy = 1 k Wh = 1000 W x (60 x 60) s
= 3.6 x 10⁶ J

\(\mathrm{H}=\mathrm{VIt}=\mathrm{I}^2 \mathrm{Rt}=\frac{V^2}{R} t\) in energy units (joules).
\(\text { or } \mathrm{H}=\frac{V I t}{J}=\frac{I^2 R t}{J}=\frac{V^2 t}{J R}\) in heat units (cal.)

Kilowatt is the unit of power. 1 kilowatt = 100 watt. Kilowatt hour is the unit of electric energy, where
1 kilowatt hour = 1000 watt x 1 hour
= 1000 watt x 60 x 60 second
= 3.6 x 10⁶ J

Normally, the potentiometer wire is made of an alloy such as nichrome or manganin. Because those alloys have high resistivity and low-temperature coefficient of resistance.

The potentiometer wire should be of uniform cross-section and composition so that there is same resistance per unit length throughout. Only then, potential difference will be proportional to length of the potentiometer wire, which is the requirement for the principle of potentiometer.

The results are most accurate, when balance point is obtained at the mid point of bridge wire. In this case R = S. The end resistances of copper strips produce least effect and the bridge is most sensitive.

There will be no depletion in the galvanometer as the condition of balanced bridge will still hold good.

Kirchhoff's first rule is based on the fact that the charges are not accumulated at a junction, i.e., the law of conservation of charge.
Kirchhoff's second rule supports the law of conservation of energy.

The units of conductance and conductivity are simen (denoted by S) and simen metre ^-1 (denoted by S m^-1) respectively. We know that conductance = 1/resistance.
We know, electrical conductivity,  \(\sigma = \frac{1}{\rho}=\frac{l}{RA}\)
If l = 1 m, R = 1 \(\Omega\), A = 1 m² then \(\sigma\) = 1 S m^-1
Thus 1 S m^-1 is the electrical conductivity of a conductor of length 1 m, area of cross-section 1 m² and resistance 1 \(\Omega\) or conductance 1S.
Dimensional formula of conductance,
\(G=\frac{1}{R}=\frac{1}{V}=\frac{[A]}{[ML^2T^{-3}A^{-1}]}=[M^{-1}L^{-2}T^{3}A^2]\)
Dimensional formula of conductivity,
\(\sigma=[M^{-1}L^{-3}T^3A^2]\)

When a person accidently touches the line wire of a 240 V supply, a current I = 240/10000 = 0.024 A = 24 mA, flows through the body of the person. This current interferes with the nerve process related to our heart beating, which is basically electrical in nature, this, in turn, accounts for a strong shock.

The value of temperature coefficient of resistance \((α)\) is more for metals than for alloys. For example, in case of copper, \(α= 4 x 10-3 oC-1 \) and for manganin, \(α= 1.5 x 10-6 oC-1.\)

Resistance = \(0.1Ω±5% = 01×10−1±5%. \)
Thus, the colour of bands in the sequence is black, brown and gold. Tolerance of \(±5%\) is indicated by a gold ring.

Silicon, germanium and carbon.

Non-ohmic devices are those devices which do not obey Ohm's law. Examples are semiconductor diode, liquid electrolyte, etc.

The best conductor is silver because electrical conductivity is inversely proportional to the resistivity and resistivity of silver is least.

The man is excited due to the transfer of electric energy to his body.

Electric current is a scalar quantity because it does not follow the laws of vectors addition, i.e., the angle between the wires carrying the current does not affect the total current in the circuit.