A length of wire is bent into a closed loop and a magnet is plunged into it, inducing a voltage and,consequently, a current in the wire. A second lenghtof wire, twice as long, is bent into two loops of wire, and a magnet is similarly plunged into it. Twice the voltage is induced, but the current is the same as that produced in the single loop. why?

The second wire has twice the resistance of the first wire. Although voltage doubles, current stays the same.

The induced voltage in a wire loop is directly proportional to the rate at which the magnetic field passing through the loop changes. When a magnet is plunged into a wire loop, the magnetic field passing through the loop increases in strength. This change in the magnetic field induces a voltage across the wire loop, which in turn generates a current.

When we double the length of the wire and bend it into two loops, the induced voltage becomes twice as much because there are now two separate wire loops. Each loop experiences a change in the magnetic field, resulting in a voltage induction.

However, although the voltage induced in the two-loop wire system is twice as much as that in the single-loop wire, the current remains the same. This happens because the current is determined by the resistance of the wire and the induced voltage. Since the two loops are connected in series, the total resistance is increased as compared to the single loop system. This increase in resistance compensates for the increased induced voltage, resulting in the same current as in the single loop.

In summary, the voltage induced in the two-loop wire system is doubled because there are two separate wire loops, but the current remains the same due to the increased resistance resulting from connecting the loops in series.

The phenomenon you are describing is known as electromagnetic induction, where the relative motion between a magnetic field and a conductor produces an induced voltage and current. In this scenario, we have two different setups: a single loop and a double loop made from a longer wire.

In the first case, a length of wire is bent into a single loop. When a magnet is plunged into it, the changing magnetic field induces a voltage in the wire. According to Faraday's law of electromagnetic induction, the induced voltage is proportional to the rate of change of magnetic flux through the loop. The induced current is then determined by the resistance of the wire and any other components in the circuit.

In the second case, a longer wire is bent into two loops, each with the same size as the single loop in the first case. When a magnet is plunged into this configuration, twice the voltage is induced compared to the single loop. However, the current remains the same.

This is because the induced voltage is determined by the rate of change of magnetic flux through the loops. Since there are now two loops instead of one, the total area enclosed by the loops is greater, which leads to a larger change in magnetic flux. Therefore, the induced voltage is doubled.

However, the resistance of the wire and the components in the circuit have not changed. According to Ohm's law (V = I * R), the current is directly proportional to the voltage and inversely proportional to the resistance. Since the resistance remains the same, the current will also remain the same, regardless of the number of loops.

In summary, the voltage induced in a loop is proportional to the rate of change of magnetic flux, which depends on the area enclosed by the loop. By doubling the area in the case of two loops, the induced voltage is also doubled. However, the current is dependent on the resistance of the circuit and remains the same in both the single loop and the double loop setups.