Physics 2001 JAMB Past Questions - Question 24: A resistance R is connected across the terminal of an electric cell of internal resistance 2Q and the voltage was reduced to 3/5 of its nominal value. The value of R is

Correct Answer

D

Explanation

When a resistance R is connected across the terminals of an electric cell with an internal resistance (r), the total resistance in the circuit becomes R + r. This forms a voltage divider circuit, and the voltage across the external resistance R can be found using the voltage divider formula:

V_R = V_nominal * (R / (R + r))

In this case, you mentioned that the voltage was reduced to 3/5 of its nominal value. So, we have:

V_R = (3/5) * V_nominal

Now, let's substitute the expression for V_R from the voltage divider formula:

(3/5) * V_nominal = V_nominal * (R / (R + r))

Now, we can solve for R:

(3/5) = R / (R + 2Q)

Now, cross-multiply:

3(R + 2Q) = 5R

Expand and simplify:

3R + 6Q = 5R

Now, move the terms with R to one side of the equation and the constant terms to the other side:

3R - 5R = -6Q

-2R = -6Q

Now, divide both sides by -2 to solve for R:

R = 3Q

So, the value of resistance R is 3 times the internal resistance 2Q, which is 6Q.