Which of the following is the symbol for a resistor?

$(a)$ 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?

$(a)$ What do the following symbols represent in a circuit? Write the name and one function of each.
$(b)$ Draw a schematic diagram of a circuit consisting of a battery of $12 \, V$,three resistors of $5 \, \Omega$,$10 \, \Omega$,and $20 \, \Omega$ connected in parallel,an ammeter to measure the total current through the circuit,and a voltmeter to measure the potential difference across the combination of resistors.
$(c)$ State any one advantage of connecting electrical devices in parallel with the mains instead of connecting them in series in a household circuit.

Compare the power used in the $2 \,\Omega$ resistor in each of the following circuits: $(i)$ a $6 \,V$ battery in series with $1 \,\Omega$ and $2 \,\Omega$ resistors,and $(ii)$ a $4 \,V$ battery in parallel with $12 \,\Omega$ and $2 \,\Omega$ resistors.

$(a)$ Explain the difference between direct current and alternating current. Write one important advantage of using alternating current.
$(b)$ An air conditioner of $2 \,kW$ is used in an electric circuit having a fuse of $10 \,A$ rating. If the potential difference of the supply is $220 \,V$,will the fuse be able to withstand the current when the air conditioner is switched on? Justify your answer.

Two resistors are connected in series as shown in the diagram. $(i)$ What is the current through the $5 \, \Omega$ resistor? (ii) What is the current through $R$? (iii) What is the value of $R$? (iv) What is the value of $V$?