$(a)$ State $Ohm's$ law. Express it mathematically.
$(b)$ Write symbols used in electric circuits to represent:
$(i)$ Variable resistance.
$(ii)$ Voltmeter.
$(c)$ An electric bulb is rated $220 \, V$ and $100 \, W$. When it is operated on $110 \, V$,what will be the power consumed?

(N/A) $Ohm's$ law states that the current flowing through a conductor is directly proportional to the potential difference across its ends,provided the temperature and other physical conditions remain constant.
Mathematically: $V = IR$,where $V$ is potential difference,$I$ is current,and $R$ is resistance.
$(b)$ $(i)$ Variable resistance: Represented by a resistor symbol with an arrow or a sliding contact.
$(ii)$ Voltmeter: Represented by a circle with a '$V$' inside,having positive and negative terminals.
$(c)$ Given: Rated power $P = 100 \, W$,Rated voltage $V = 220 \, V$.
First,calculate the resistance of the bulb:
$R = \frac{V^2}{P} = \frac{(220)^2}{100} = \frac{48400}{100} = 484 \, \Omega$.
Now,calculate the power consumed at $V_1 = 110 \, V$:
$P_{new} = \frac{V_1^2}{R} = \frac{(110)^2}{484} = \frac{12100}{484} = 25 \, W$.
The power consumed will be $25 \, W$.