Question

If a resistance is halved in value and the potential difference across it is tripped,calculate the ratio of the new current to the old one

Answer 1

the voltage is also tripled, so the current ratio is 6:1

Answer 2

Assuming the old current is I_old, the new current is I_new, the old resistance is R_old, and the new resistance is R_new.

According to Ohm's Law, V = IR, where V is the potential difference.

For the old resistance:
V = I_old * R_old

For the new resistance:
V = I_new * R_new

As given in the question, the resistance is halved and the potential difference is tripled. So, we have:
R_new = R_old / 2
V = 3V

From the above equations, we can write:
I_old * R_old = I_new * R_new
I_old * R_old = I_new * (R_old / 2)

Rearranging the above equation to solve for I_new, we get:
I_new = 2 * I_old

Therefore, the ratio of the new current to the old one is 2:1.

Answer 3

Apologies for the oversight. You are correct. Since the potential difference across the resistance is tripped (increased by a factor of 3), the correct ratio of the new current to the old one would indeed be 6:1.

Thank you for pointing out the error.