Refer to the circuit diagram given in the figure, which of the following observations are correct?
Observations:
A. Total resistance of circuit is 6 Ω
B. Current in Ammeter is 1 A
C. Potential across AB is 4 Volts
D. Potential across CD is 4 Volts
E. Total resistance of the circuit is 8 Ω
Choose the correct answer from the options given below:
Show Hint
When analyzing circuits, always use Ohm’s law to calculate current and voltage drops across resistors. Series resistances add up, and the voltage is divided among the resistors in proportion to their resistance.
To address the problem, a step-by-step analysis of the provided circuit and observations is performed.
The circuit comprises a 6V battery and three 4 Ω resistors.
Total circuit resistance calculation:
Resistors between CD and CB are connected in series, yielding a combined resistance of \(R_{series} = 4 \Omega + 4 \Omega = 8 \Omega\).
This series arrangement is in parallel with resistor AB (4 Ω).
The equivalent resistance of this parallel combination is calculated as \(R_{parallel} = \frac{1}{\frac{1}{8} + \frac{1}{4}} = \frac{1}{\frac{1 + 2}{8}} = \frac{8}{3} \Omega \approx 2.67 \Omega\).
Adding the resistance of resistor AC (4 Ω) in series results in the total resistance: \(R_{total} = 4 \Omega + 2.67 \Omega \approx 6.67 \Omega\).
Ammeter current calculation:
Ohm's Law is applied: \(I = \frac{V}{R} = \frac{6}{6.67} \approx 0.9 A\).
Potential difference across AB:
The voltage drop across the 4 Ω resistor (either preceding or following the parallel section) is: \(V_{AB} = I \times 4 = 0.9 \times 4 \approx 3.6 \, \text{Volts}\).
