A light bulb has a solid cylindrical filament of length l and radius a and consumes power p. We have to design a new bulb, using cylindrical filament of same material, operating at same voltage and emitting the same spectrum of light, which will consume power np. The new length and radius of filament are (loss due to convection is minimal, temperature of filament is uniform).
Answers
The new Area (A) - Length (L) ratio is n times that of earlier.
•The Ohm's Law says:
Current (I) in a circuit is directly proportional to the voltage (V) across it. The constant of proportionality being the resistance (R) offered by the circuit.
Hence, V = I R
•We know power (P) consumed is:
P = I V
Substituting for I from Ohm's Law:
P = V² / R ...(1)
•Now, we know resistance (R) is given by:
R = ρ L / A ...(2)
Where L is length and A is cross sectional area.
•Putting (2) in (1),
P = V² A / ρ L
•According to question the new power is nP, voltage remains same and the material remains same, hence,
nP = V² A / ρ L
→ n( P ρ / V²) = A / L
Hence, the new Area (A) - Length (L) ratio is n times that of earlier.