Two batteries of emf's and internal resistances 0.2 Ω 0.4 Ω are connected in parallel. This combination is connected to a 4 Ω resistor. Find: (i) the equivalent emf of the combination (ii) the equivalent internal resistance of the combination (iii) the current drawn from the combination
Official Solution
Correct Option: (1)
For two batteries connected in parallel, the equivalent emf and equivalent internal resistance are given by: Given: , ,
(i) Equivalent emf:
(ii) Equivalent internal resistance:
(iii) Current drawn from the combination: The total resistance of the circuit is: The current is: ---
02
PYQ 2025
medium
physicsID: cbse-cla
Four resistors, each of resistance R and a key K are connected as shown in the figure. The equivalent resistance between points A and B when key K is open will be:
1
2
3
4
Official Solution
Correct Option: (4)
Step 1: Identify Nodes
The outer circular wire is a perfect conductor, so all points on it are at the same potential. Therefore, the left, top, bottom, and right boundary points are all the same node as B.
Let the center junction be node C. Point A is connected to C through one resistor R.
Step 2: Resistance between C and B
From the central node C to the outer node B, there are three resistors of resistance R connected:
One resistor from C to the left boundary
One resistor from C to the top boundary
One resistor from C to the bottom boundary
Since all boundary points are the same node (outer wire), these three resistors are in parallel.
RCB = R || R || R
1/RCB = 1/R + 1/R + 1/R = 3/R
RCB = R/3
Step 3: Total resistance between A and B
The point A is connected to C via one resistor R. Then from C to B the equivalent resistance is R/3.
