SATHEE: current-electricity Question 17

Current Electricity

current-electricity Question 17

Question: Q. 4. Two metallic wires $P_{1}$ and $P_{2}$ of the same material and same length but different cross-sectional areas $A_{1}$ and $A_{2}$ are joined together and then connected to a source of emf. Find the ratio of the drift velocities of free electrons in the wires $P_{1}$ and $P_{2}$ , if the wires are connected (i) in series, and (ii) in parallel.

U] [Foreign II 2017]

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Solution:

Ans. Ratio of drift velocities in series 1

Ratio of drift velocities in parallel

In series, the current remains the same

$\begin{aligned} I & = n e A_{1} v_{d_{1}} = n e A_{2} v_{d_{2}} ∴ & \frac{v_{d 1}}{v_{d 2}} & = \frac{A_{2}}{A_{1}} \end{aligned}$

In parallel potential difference is same but currents are different.

$\begin{array}{ll} I_{1} R_{1} = I_{2} R_{2} ∴ \frac{v_{d 1}}{v_{d 2}} = 1 \end{array}$

$\begin{aligned} V & = I_{1} R_{1} & = n e A_{1} v d_{1} \frac{ρ l}{A_{1}} & = n e ρ v_{d 1} l V & = I_{2} R_{2} = n e ρ v_{d 2} l R_{1} & = I_{2} R_{2} \frac{11}{12} & = 1 \end{aligned}$

[CBSE Marking Scheme 2017]

Current Electricity

current-electricity Question 17

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Current Electricity

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