$A$ hot plate of an electric oven connected to a $220 \ V$ line has two resistors $A$ and $B$ each of $22 \ \Omega$ resistance. These resistors may be used separately,in series,or in parallel. Find the current flowing in all the three cases.

$(a)$ Three resistors $R_{1}, R_{2}$ and $R_{3}$ are connected in parallel and the combination is connected to a battery,ammeter,voltmeter,and key. Draw a suitable circuit diagram. Obtain an expression for the effective resistance of the combination of resistors in parallel.
$(b)$ Why are electric bulbs filled with chemically inactive nitrogen or argon?
$(c)$ What is meant by the statement that the rating of a fuse in a circuit is $5 \ A$?

$(a)$ 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?

Read the following statements carefully and state whether each statement is true or false:
$(i)$ The quantity of charge flowing past a point multiplied by time is current.
$(ii)$ The flow of charge through a conducting wire connected to a cell is the result of a chemical reaction inside the cell.
$(iii)$ The resistivity of all pure metals increases with an increase in temperature.
$(iv)$ Ohm's law is a relation between the power used in a circuit to the current and the potential difference.
$(v)$ $A$ series circuit has only one conducting path for the electrons that move through it; a parallel circuit has multiple conducting paths.
$(vi)$ $A$ conducting wire offers resistance to the flow of electrons because electrons repel each other in the wire.

$(a)$ Name an instrument that measures potential difference between two points in a circuit. Define the unit of potential difference in terms of $SI$ unit of charge and work. Draw the circuit symbols for $(i)$ variable resistor,$(ii)$ a plug key which is closed.
$(b)$ Two electric circuits $(I)$ and $(II)$ are shown below.
$(i)$ Which of the two circuits has more resistance?
$(ii)$ Through which circuit does more current pass?
$(iii)$ In which circuit is the potential difference across each resistor equal?
$(iv)$ If $R_{1} > R_{2} > R_{3}$,in which circuit will more heat be produced in $R_{1}$ as compared to the other two resistors?

$(a)$ Calculate the resistance of the wire using the graph.
$(b)$ How many $176 \,\Omega$ resistors in parallel are required to carry $5\, A$ on a $220\, V$ line?
$(c)$ Define electric power. Derive the relation between power,potential difference,and resistance.