A wire of length 5 m and resistance 20 ohm is cut to make 5 pieces of equal length. Can they all be used to make a resistor of 5 ohm?
The wire of length 5 m has a resistance of 20 ohm. It is cut into five equal pieces. Assuming the radius and resistivity is constant throughout the wire, each piece has a resistance of 4 ohm. They have to be joined to yield a resistor with resistance 5 ohm.
This is not possible to accomplish merely by connecting the wires in parallel or series as we get resistors with a resistance (5*(1/4))^-1 = 4/5 ohm and 20 ohm respectively.
One of the pieces can be used to get 4 ohm. The other four pieces can be connected in parallel we get an equivalent resistance of (4*(1/4))^-1 = 1 ohm.
The piece with a resistance of 4 ohm and the set created with a resistance of 1 ohm can be joined in series to get a resistor with a resistance of 5 ohm.