Question

The filament of a bulb takes a current 0.1 A when potential difference across it is 0.2 V. When the potential difference across it becomes 1.0 V, the current becomes 0.4 A. The resistance of filament in each case will be

• A. $2.0\Omega$, $2.5\Omega$
• B. $2.5\Omega$, $2\Omega$
• C. $1.0\Omega$, $2.5\Omega$
• D. $2.0\Omega$, $2\Omega$

Answer 1

The correct option is A $2.0\Omega$, $2.5\Omega$

Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points. Introducing the constant of proportionality, the resistance, we arrive at the usual mathematical equation that describes this relationship: $I=\frac{V}{R}$, where, I is the current through the conductor in units of amperes, V is the potential difference measured across the conductor in units of volts, and R is the resistance of the conductor in units of ohms.

Therefore, $R=V/I.$

In the first case, the voltage is o.2 V and the current is 0.1 A. So, the resistance is 2 ohms. In the second case, the voltage is 1 V and the current is 0.4 A. So, the resistance is 2.5 ohms.

The current in the wire is due to the drifting of electrons inside a wire in a direction opposite to the flow of electrons. During their drifting, they collide with their atoms vibrating about their mean position and lose some of the kinetic energy to the vibrating atoms which increase the amplitude of the vibration of the atoms, and the thermal energy of the metal increases and hence we observe the corresponding rise in temperature of the wire.