A heating filament and an ideal resistor of fixed value are connected in series with a DC voltage source. After some time, the filament has reached its operating point so that the current in the circuit is steady. Which one of the following is correct?
The steady voltage across the ideal resistor decreases as compared to its initial value.
When the DC source is switched on, the filament is cold and has low resistance, so the initial current is high. As current flows, \(I^2R\) heating raises the filament's temperature, and since it has a positive temperature coefficient of resistance, its resistance increases until the operating point (steady state) is reached. As the filament's resistance rises, the total series resistance \(R_{total} = R_{filament} + R\) increases, so the current in the circuit decreases from its initial (cold) value to a lower steady value. Since the resistor is ideal (fixed resistance), the steady voltage across it, \(V_R = IR\), decreases in the same proportion as the current. Hence option (b) is correct; options (a), (c) and (d) describe the opposite trend.
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