(a) (i) The potential difference across the two ends of a circuit component is decreased to one-third of its initial value, while its resistance…

The potential difference across the two ends of a circuit component is decreased to one-third of its initial value, while its resistance remains constant. What change will be observed in the current flowing through it ? Name and state the law which helps us to answer this question.

Draw a schematic diagram of a circuit consisting of a battery of four $\displaystyle 1 \cdot 5 \mathrm{~V}$ cells, a $\displaystyle 5 \Omega$ resistor, a $\displaystyle 10 \Omega$ resistor and a $\displaystyle 15 \Omega$ resistor and a plug key, all connected in series. Now find

the electric current passing through the circuit, and

potential difference across the $\displaystyle 10 \Omega$ resistor when the plug key is closed.

When is the potential difference between two points said to be $\displaystyle 1$ volt?

A copper wire has a diameter of $\displaystyle 0 \cdot 2 \mathrm{~mm}$ and resistivity of $\displaystyle 1 \cdot 6 \times 10^{-8} \Omega \mathrm{~m}$. What will be the length of this wire to make its resistance $\displaystyle 14 \Omega$ ? How much does the resistance change, if the diameter of the wire is doubled ?