An electric oven hot plate is connected to a $200 \, V$ line. It has two resistance coils $A$ and $B$,each of $30 \, \Omega$,which may be used separately,in series,or in parallel. Find the value of the current required in each of the three cases.

Two electric circuits $I$ and $II$ are shown in the figure.
$(i)$ 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?

$(a)$ Derive an expression to find the equivalent resistance of three resistors connected in series. Also,draw the schematic diagram of the circuit.
$(b)$ Find the equivalent resistance of the following circuit.

Explain the following.
$(a)$ Why is the series arrangement not used for domestic circuits?
$(b)$ How does the resistance of a wire vary with its area of cross-section?

In the given circuit,calculate $(i)$ total resistance of the circuit,and (ii) current shown by the ammeter.

$(a)$ 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?