Rankers Physics

Combination of Resistors: Practice Problem & Solution

Assertion (A): When two conducting wires of different resistivity having same cross section area are joined in series, the electric field in them would be equal when they carry current. Reason (R): When wires are in series they carry equal current.  
(1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
(2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(3) (A) is true but (R) is false
(4) Both (A) and (R) are false

Solution Explained:

To solve this problem, we apply the core principles of Combination of Resistors. Understanding the underlying formula is key to arriving at the correct answer below:

Concept: Relationship between electric field, resistivity, current density.
Formula: \(E = \rho J = \rho (I/A)\).
Solution: In series, current \(I\) and cross-section \(A\) are same. Electric field \(E = \rho (I/A)\). Since resistivities \(rho\) are different, electric fields \(E\) must be different. Thus, A is false and R is true.

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