State $Ohm's$ law. Write the mathematical representation of $Ohm's$ law. Use this relationship to define $1\, ohm.$ List two disadvantages of connecting different electrical appliances in series.
$Ohm's law$ : The potential difference across the ends of a resistor is directly proportional to the current through it, provided its temperature remains the same.
$V = IR$ or $R = V / I$
$1\, ohm =1$ volt $/,1$ ampere
If the potential difference across the two ends of a conductor is $1\, V$ and the current through it is $1\, A,$ then the resistance $R$ of the conductor is $1\, ohm$
$(i)$ Different electric appliances need currents of widely different values to operate properly which they do not get if joined in series.
$(ii)$ When one appliance fails, the circuit is broken and none of the appliance works.
Draw the nature of $V -I$ graph for a nichrome wire. $(V -$ Potential difference, $I -$ Current)
$A$ metallic wire of $625\, mm$ length offers a $4\, \Omega$ resistance. If the resistivity of the metal is $4.8 \times 10^{-7} \,ohm-metre$, then calculate the area of cross$-$ section of the wire.
$(a)$ How much current will an electric bulb draw from a $220\, V$ source, if the resistance of the bulb filament is $1200\,ohm$ ?
$(b)$ How much current will an electric heater coil draw from a $220\, V$ source, if the resistance of the heater coil is $100\, ohm$ ?
Find out the following in the electric circuit given in figure
$(a)$ Effective resistance of two $8\, \Omega$ resistors in the combination.
$(b)$ Current flowing through $4\, \Omega$ resistor.
$(c)$ Potential difference across $4\, \Omega$ resistor.
$(d)$ Power dissipated in $4\, \Omega$ resistor.
$(e)$ Difference in ammeter readings, if any.
$V-I$ graph for a given metallic wire at two temperatures are shown, which of these is for a higher temperature ?
When do we say that the resistors are connected in parallel ?