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.

Find out the following in the electric circuit given in the figure:
$(a)$ Effective resistance of two $8\,\Omega$ resistors in the combination.
$(b)$ Current flowing through the $4\,\Omega$ resistor.
$(c)$ Potential difference across the $4\,\Omega$ resistor.
$(d)$ Power dissipated in the $4\,\Omega$ resistor.
$(e)$ Difference in ammeter readings,if any.

Explain the following.
$(a)$ Why is the series arrangement not used for domestic circuits?
$(b)$ How does the resistance of a wire vary with its area of cross-section?

Draw a circuit diagram of an electric circuit containing a cell,a key,an ammeter,a resistor of $2\,\Omega$ in series with a combination of two resistors ($4\,\Omega$ each) in parallel and a voltmeter across the parallel combination. Will the potential difference across the $2\,\Omega$ resistor be the same as that across the parallel combination of $4\,\Omega$ resistors? Give reason.

$A$ current of $1 \ A$ flows in a series circuit containing an electric lamp and a conductor of $5 \ \Omega$ when connected to a $10 \ V$ battery. Calculate the resistance of the electric lamp. Now,if a resistance of $10 \ \Omega$ is connected in parallel with this series combination,what change (if any) in the current flowing through the $5 \ \Omega$ conductor and the potential difference across the lamp will take place? Give reason.

$(a)$ Calculate the resistance of the wire using the graph.
$(b)$ How many $176 \,\Omega$ resistors in parallel are required to carry $5\, A$ on a $220\, V$ line?
$(c)$ Define electric power. Derive the relation between power,potential difference,and resistance.