Three identical resistors are connected first in series to an electrical voltage V. Let I be the total current flowing in the circuit. These resistors are disconnected and again connected in parallel with the same source. Which of the following statements are true?
(A) The potential difference across each resistor is V/3 in series connection
(B) The potential difference across all three resistors in parallel connection is 3V
(C) The current flowing in each resistor in series connection is the same as I
(D) The current flowing through each resistor in parallel combination is equal to 3I
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A), (C) and (D) only
Let each resistor be \( R \). In series the same current flows through all three and the voltage divides; in parallel each resistor gets the full voltage.
\( \displaystyle I = \frac{V}{3R} \)
(A) The potential difference across each resistor is V/3 in series connection — Correct. Each resistor has \( IR = \frac{V}{3R}\,R = V/3 \).
(B) The potential difference across all three resistors in parallel connection is 3V — Incorrect. In parallel each resistor is connected directly across the source, so the potential difference across each is \( V \), not \( 3V \).
(C) The current flowing in each resistor in series connection is the same as I — Correct. A series circuit has only one path, so the same current \( I \) flows through every resistor.
(D) The current flowing through each resistor in parallel combination is equal to 3I — Correct. Each resistor now carries \( V/R \), and \( V/R = 3 \times \frac{V}{3R} = 3I \).