A potential difference is applied across the filament of a bulb at t =0, and it is maintained at a constant value while the filament gets heated to its equilibrium temperature. We find that the final current in the filament is one sixth of the current drawn at t = 0. if the temperature of the filament at t = 0 is `20^@C` and the temperature coefficient of resistivity at `20^@C` is `0.0043 ^@C^(-1),` find the final temperature of the filament.

Explanation

To solve the problem step by step, we will follow the reasoning and calculations as outlined in the video transcript.

### Step 1: Understand the relationship between current and resistance
At time \( t = 0 \), the current \( I_0 \) is drawn through the filament. The final current \( I_f \) is given as one sixth of the initial current:
\[ I_f = \frac{1}{6} I_0 \]
According to Ohm's law, \( I = \frac{V}{R} \), where \( V \) is the constant potential difference applied across the filament and \( R \) is the resistance. Since the voltage is constant, the relationship between the currents and resistances can be expressed as:
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