$(a)$ 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, $a$ 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.
$(a)$ $(i)$ A variable resistor or rheostat. Used to vary current in a circuit.
$(ii)$ Wires crossing without joining. Used when different parts of the circuit are to be connected without joining all of them.
$(b)$ The circuit diagram is as shown below
$(c)$ $(i)$ When the devices are connected in parallel, then even if one device fails, the others keep on working
$(ii)$ In parallel, the potential across each device is same.
A piece of wire having resistance $R$ is cut into four equal parts. $(a)$ How will the resistance of each part compare with the original resistance ? $(b)$ If the four parts are placed in parallel, how will the joint resistance compare with the resistance of the original wire ?
A nichrome wire has a resistance of $10\, \Omega$. Find the resistance of another nichrome wire, whose length is three times and area of cross-section four times the first wire.
What is meant by resistance of a conductor ? Name and define its $SI$ unit. List the factors on which the resistance of a conductor depends. How is the resistance of a wire affected if
$(i)$ its length is doubled,
$(ii)$ its radius is doubled. ?
$(a)$ In the circuit shown connect a nichrome wire of length ${ }^{\prime \prime} L^{\prime \prime}$ between points $X$ and $Y$ and note the ammeter reading.
$(i)$ When this experiment is repeated by inserting another nichrome wire of the same thickness but twice the length $(2 L),$ what changes are observed in the ammeter reading ?
$(ii)$ State the changes that are observed in the ammeter reading if we double the area of cross-section without changing the length in the above experiment. Justify your answer in both the cases.
$(b)$ "Potential difference between points $A$ and $B$ in an electric field is $1\, V^{\prime \prime} .$ Explain the statement.
$100 \,J$ of heat is produced each second in a $4\, \Omega$ resistance. Find the potential difference across the resistor.