Two metallic wires of the same material have the same length but cross-sectinal area is in the ratio of 1:2.they are connected in
1)-series
2)-parallel.
Compare the drift velocities of the electrons in the two wires in both the cases.
Plzz help
series - 2:1
parallel - 1:1
Two wires A and B of the same material and having same length, have their
cross sectional areas in the ratio 1:6. What would be the ratio of heat produced
in these wires when same voltage is applied across each?
A1/A2=1/6
H = I2RT
H=V2T/R
R=PL/A
H1/H2=1/6
To compare the drift velocities of the electrons in the two wires connected in series and parallel, we need to understand the concepts of current, resistance, and drift velocity.
1) Series Connection:
In a series connection, the two wires are connected one after the other, forming a single path for the electric current to flow through. Therefore, the total resistance in the circuit is the sum of the resistances of the individual wires.
The resistance of a wire depends on its length, cross-sectional area, and the resistivity of the material:
Resistance (R) = (Resistivity × Length) / Cross-sectional area
Given that the length of both wires is the same, and the cross-sectional area is in the ratio of 1:2, we can assume that the wire with the larger area has half the resistance compared to the wire with the smaller area.
The current (I) flowing through the circuit is the same in both wires, as it is a series connection. According to Ohm's Law, I = V/R, where V is the potential difference across the circuit.
The drift velocity (v) of electrons in a wire is given by the formula: v = I / (nAe), where n is the number density of free electrons in the wire, A is the cross-sectional area of the wire, and e is the charge of an electron.
Since the current is the same in both wires, we can compare the drift velocities based on the factors that affect it: cross-sectional area (A) and the charge of an electron (e).
2) Parallel Connection:
In a parallel connection, the two wires are connected side by side, providing separate paths for the electric current to flow through. Therefore, the potential difference (V) across both wires is the same.
The total current flowing through the circuit is the sum of the currents in each wire. Using Ohm's Law (I = V/R), we can find the individual currents in each wire.
Since the current is different in each wire, we need to calculate the drift velocities separately using the formula: v = I / (nAe).
Summarizing the comparisons:
1) Series Connection:
- The current (I) is the same in both wires.
- The drift velocity (v) will be higher in the wire with the smaller cross-sectional area because it has a higher resistance.
2) Parallel Connection:
- The potential difference (V) is the same across both wires.
- The current (I) will be different in each wire due to their different resistances.
- The drift velocity (v) will be higher in the wire with the smaller resistance, i.e., the wire with the larger cross-sectional area.
In conclusion, the drift velocities of the electrons will differ in both cases due to the variations in resistance and cross-sectional area. The actual comparison would depend on the specific values of resistance, cross-sectional area, and other variables involved.