What is the electrical resistivity of a material? What is its $SI$ unit? Describe an experiment to study the factors on which the resistance of a conducting wire depends.

What is the resistance of an ideal voltmeter?

Three resistors $R_{1}$,$R_{2}$,and $R_{3}$ are connected in parallel between points $A$ and $B$. The equivalent resistance $R$ is given by:

$(a)$ 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?

Who invented the simple battery?

Draw a circuit diagram for a circuit consisting of a battery of five cells of $2 \text{ V}$ each, a $5 \, \Omega$ resistor, a $10 \, \Omega$ resistor, and a $15 \, \Omega$ resistor, an ammeter, and a plug key; all connected in series. Also, connect a voltmeter to record the potential difference across the $15 \, \Omega$ resistor and calculate:
$(i)$ the electric current passing through the above circuit and
$(ii)$ the potential difference across the $5 \, \Omega$ resistor when the key is closed.