Assuming that voltage remains constant, what happens to the current in a filament if it is replaced by a thinner wire?

A. The current increases.
B. The current decreases.
C. The current is not affected by a change in filament thickness.
D. The current alternates between high and low values

Question

Assuming that voltage remains constant, what happens to the current in a filament if it is replaced by a thinner wire?

 		A.	The current increases.
 		B.	The current decreases.
 		C.	The current is not affected by a change in filament thickness.
 		D.	The current alternates between high and low values

anonymous · Answer

The resistance of a wire is given by:$$R=\frac{ \rho L }{ A}$$where R is the resistance; ρ is the resistivity (an intrinsic property of the wire material); L is the length of the wire; and A is the cross-sectional area of the wire.  Alas, you need to to know happens to current.  So let's write Ohm's law as follows:$$I=\frac{ V }{ R }$$And now let's insert the first equation into our second:$$I=\frac{ VA }{ \rho L }$$Voltage is constant; L is constant; and ρ is constant.  The only things varying are the current, I, and the cross sectional area,  A.  Now, a thinner wire has a smaller A, so to answer your question, in our last equation, what happens to I as A gets small?