A nichrome wire X with length (l) & cross-sectional area (A) is connected to a 10 V source and another nichrome wire Y with length (2l) & cross-sectional area (A/2), is connected to a 20 V source.
(a) Compare the resistances of wires X and Y. [Given that the resistivity of nichrome is (ρ).]
(b) Compare the electrical power consumed by each wire.
(c) Compare the masses of these wires. (Given that the density of nichrome is d.)
(d) State True or False : Wire X and wire Y both show the same rise in temperature in the same time.

Question

A nichrome wire X with length (l) & cross-sectional area (A) is connected to a 10 V source and another nichrome wire Y with length (2l) & cross-sectional area (A/2), is connected to a 20 V source.
(a) Compare the resistances of wires X and Y. [Given that the resistivity of nichrome is (ρ).]
(b) Compare the electrical power consumed by each wire.
(c) Compare the masses of these wires. (Given that the density of nichrome is d.)
(d) State True or False : Wire X and wire Y both show the same rise in temperature in the same time.

KnowledgeBoat · Accepted Answer

Given, - Length of nichrome wire X (lX) = l - Cross-sectional area of nichrome wire X (AX) = A - Potential difference across nichrome wire X (VX) = 10 V - Length of nichrome wire Y (lY) = 2l - Cross-sectional area of nichrome wire Y (AY) = A/2 - Potential difference across nichrome wire Y (VY) = 20 V - resistivity of nichrome = ρ (a) Let 'RX' and 'RY' be the resistance of nichrome wire X and Y respectively. Now, And As, So, RX : RY = 1 : 4 (b) And So, PX : PY = 1 : 1 (c) Given, Mass density of nichrome = d Then, Mass of wire X (mX) = d x volume = d x Al And, Mass of wire Y (mY) = d x volume = d x 2l x = d x Al = mX So, mX : mY = 1 : 1 (d) True. Reason Let, heat gained by the wire X be 'QX' and change in temperature be 'ΔTX'. Similarly, heat gained by the wire Y be 'QY' and change in temperature be 'ΔTY'. Again, let specific heat capacity of nichrome be 'c' and same time be 't'. Then, QX = PX x t = mXc x ΔTX and QY = PY x t = mYc x ΔTY As, PX = PY then QX = QY for same time t. ⇒ mXc x ΔTX = mYc x ΔTY ⇒ mX x ΔTX = mY x ΔTY So, ΔTX : ΔTY = mX : mY = 1 : 1 Hence, wire X and wire Y both show the same rise in temperature in the same time.

Physics

Current Electricity

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Physics

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