Physics 2011 JAMB Past Questions - Question 37: Three similar cells each of e.m.f 2V and internal resistance 2Ω are connented in parallel , total e.m.f and total internal resistance

Correct Answer

D

Explanation

To find the total electromotive force (e.m.f) and total internal resistance of the three similar cells connected in parallel, we can use the following formulas:

Total e.m.f (E_total) = E_1 + E_2 + E_3
Total internal resistance (R_total) = R_1 // R_2 // R_3

Given that each cell has an e.m.f of 2V and an internal resistance of 2Ω, we can substitute these values into the formulas:

Total e.m.f (E_total) = 2V + 2V + 2V = 6V
Total internal resistance (R_total) = 2Ω // 2Ω // 2Ω

To calculate the total internal resistance, we need to find the equivalent resistance of the three resistors connected in parallel. The formula for calculating the equivalent resistance of two resistors in parallel is:

R_eq = (R_1 * R_2) / (R_1 + R_2)

Using this formula, we can calculate the equivalent resistance for the first two resistors:

R_eq_1_2 = (2Ω * 2Ω) / (2Ω + 2Ω) = 4Ω / 4Ω = 1Ω

Now, we can calculate the equivalent resistance of the third resistor (R_eq_1_2) in parallel with the third resistor (2Ω):

R_total = (1Ω * 2Ω) / (1Ω + 2Ω) = 2Ω / 3Ω = 0.67Ω (rounded to two decimal places)

Therefore, the total e.m.f of the three cells connected in parallel is 6V, and the total internal resistance is approximately 0.67Ω.