Which of the following statements is false? The sum of the potential drops across resistors A, D and E is the same as the potential gain across the source of emf. The sum of the potential drops across resistors B and C is the same as the potential gain across the source of emf. The sum of the potential drops across resistors B and C is the same as the potential drop across resistor D.
The correct answer and explanation is:
The false statement is:
The sum of the potential drops across resistors B and C is the same as the potential drop across resistor D.
Explanation (300 words):
In any electrical circuit, Kirchhoff’s Voltage Law (KVL) states that the total sum of the potential differences (voltages) around any closed loop is zero. This means that the sum of the potential drops across all elements in a loop equals the total emf (electromotive force) provided by the source. This law is fundamental to analyzing electrical circuits.
Let’s examine the statements one by one:
- “The sum of the potential drops across resistors A, D, and E is the same as the potential gain across the source of emf.”
- This follows directly from KVL. If resistors A, D, and E are in series with the emf source in a closed loop, the total voltage across them must equal the source voltage. ✔️ True
- “The sum of the potential drops across resistors B and C is the same as the potential gain across the source of emf.”
- Again, if B and C are in series and part of a closed loop with the emf source, this would be true. It implies that B and C together account for the entire emf, which can happen depending on circuit design. ✔️ True
- “The sum of the potential drops across resistors B and C is the same as the potential drop across resistor D.”
- This is not necessarily true and is generally false unless there’s a very specific circuit configuration (e.g., a balanced bridge). In most circuits, resistor D is in a different loop or branch than B and C, so their voltage drops aren’t guaranteed to match. ❌ False
This last statement conflicts with KVL and Ohm’s Law unless additional constraints (like symmetry or bridge balance) are imposed. Therefore, it is the false statement.