(2)

Consumption of electrical energy in 3 hours can be calculated by using the formula:

$$\begin{gathered} E=P\times t \\ = 2 \hspace{0.17em} kW \times 3 \hspace{0.17em} hours = 6 \hspace{0.17em} kWh \end{gathered}$$

Unit cost of electrical energy

$=4per kWh$

Therefore, the cost of energy used for three hours will be:
$4\times 6=24$

(2)

An ampere is the SI unit of electric current.

$$\begin{gathered} 1 A = 1000 mA or 1 mA =\frac{1}{1000} A={10}^{-3} A \\ Thus, 1\mu A={10}^{-3}\times {10}^{-3} A={10}^{-6} A \end{gathered}$$

(1)

Resistance of a resistor $R\Omega$

New resistance of a resistor $\frac{R}{2}\Omega$

All other parameters of the circuit remain unchanged.

By applying Joule’s law of heating: $H=I^{2}Rt$

$As per Ohm’s law 𝑉 = 𝐼R$

$$\begin{gathered} or 𝐼 = 𝑉/𝑅 \\ H=\frac{V}{R}\times \frac{V}{R}\times R\times t=\frac{V^2}{R}\times t \\ Case I: H=\frac{V^2}{R}\times t \\ Case II: H\text{'}=\frac{V^2}{{\displaystyle \frac{R}{2}}}\times t \\ =\frac{V^2\times 2}{R}\times t \\ H\text{'}=H\times 2 \end{gathered}$$

Hence, the heating effect in the resistor will become two times if all other parameters of the circuit remain the same.

(1)

An electric fuse is connected with the live wire because it gets blown up when an excess current tries to pass through it in order to save the electrical appliances by restricting the flow of that current.

(2)

We know that, P=VI…(i)

Where,
P =  Power
V = Potential difference
I = Current
V = IR …(ii)

On substituting equation (ii) in equation (i), we get:

$P=I^{2}R\dots \left(iii\right)$

Again, from Ohm's law:

$I=V/R \dots \left(iv\right)$

On substituting equation (iv) in equation (i), we get:

$P=\frac{V^2}{R}$

Hence, option (b) $I{R}^2$ does not represent power

(3)

If the temperature of the entire system increases when the current is flowing through a metallic wire, the power (VI) is dissipated in the form of heat. Hence, the potential difference (V) decreases.

(2)

Electric power, $P=VI=I^{2}R=\frac{V^2}{R}$

Electrical Energy $=Pt=VIt=I^{2}Rt=\frac{V^{2}t}{R}$