Question

The current through a \(\frac{4}{3}\Omega\) external resistance connected to a parallel combinationof two cells of 2 V and 1 V emf and internal resistances of 1 \(\Omega\) and 2 \(\Omega\) respectively is ______.
Fill in the blank with the correct answer from the options given below

• A. 1A
• B. \(\frac{2}{3}A\)
• C. \(\frac{3}{4}A\)
• D. \(\frac{5}{6}A\)

Answer 1

The Correct Option is D

To solve this problem, we need to find the equivalent emf and equivalent internal resistance of the parallel combination of the two cells.

Given:

• E1 = 2 V, r1 = 1 Ω
• E2 = 1 V, r2 = 2 Ω
• R = 4/3 Ω (external resistance)

1. Equivalent Internal Resistance (r):

For parallel resistors:

1/r = 1/r1 + 1/r2

1/r = 1/1 + 1/2

1/r = 3/2

r = 2/3 Ω

2. Equivalent EMF (E):

For parallel cells:

E/r = E1/r1 + E2/r2

E/(2/3) = 2/1 + 1/2

E * (3/2) = 5/2

E = (5/2) * (2/3)

E = 5/3 V

3. Total Resistance (R_total):

R_total = r + R

R_total = 2/3 + 4/3

R_total = 6/3 = 2 Ω

4. Current (I):

I = E / R_total

I = (5/3) / 2

I = 5 / (3 * 2)

I = 5/6 A

Therefore, the current through the 4/3 Ω external resistance is 5/6 A.

The correct answer is:

Option 4: 5/6 A