What is potential difference? Is it a scalar quantity or a vector quantity? Give its $SI$ units.

$(a)$ Name an instrument that measures electric current in a circuit. Define the unit of electric current.
$(b)$ What do the following symbols mean in circuit diagrams?
$(c)$ An electric circuit consisting of a $0.5 \ m$ long nichrome wire $XY$,an ammeter,a voltmeter,four cells of $1.5 \ V$ each and a plug key was set up.
$(i)$ Draw a diagram of this electric circuit to study the relation between the potential difference maintained between the points $X$ and $Y$ and the electric current flowing through $XY$.
$(ii)$ The following graph was plotted between $V$ and $I$ values. What would be the values of $V/I$ ratios when the potential difference is $0.8 \ V$,$1.2 \ V$ and $1.6 \ V$ respectively? What conclusion do you draw from these values?

An electric bulb rated $220 \, V, 60 \, W$ is working at full efficiency. $(i)$ State the resistance of the coil of the bulb. Another identical bulb is connected in series with the first one and the system is connected across the mains as shown below. $(ii)$ State the rate of conversion of energy in each bulb. $(iii)$ Calculate the total power. $(iv)$ What will be the total power if the bulbs are connected in parallel?

Study the $V - I$ graph for a resistor as shown in the figure and prepare a table showing the values of $I$ (in amperes) corresponding to four different values of $V$ (in volts). Find the value of current $I$ (amperes) for $V=10$ volts. How can we determine the resistance of the resistor from this graph?

Why do the wires connecting an electric heater to the mains not glow while its heating element does?

What are the units of resistance?