Question

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:

• A. A, B and D only
• B. A, C and D only
• C. B, C and E only
• D. A, B and C only

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.

Answer 1

The Correct Option is A

To solve the problem, let's analyze the given circuit and observations step-by-step.

The circuit consists of a battery of 6V and three resistors each of 4 Ω.

1.  Calculate the total resistance of the circuit:
   • Resistors between CD and CB are in series, making their total resistance \(R_{series} = 4 \Omega + 4 \Omega = 8 \Omega\).
   • This series combination is in parallel with the resistor AB which is 4 Ω.
   • Equivalent resistance of the parallel combination, \(R_{parallel} = \frac{1}{\frac{1}{8} + \frac{1}{4}} = \frac{1}{\frac{1 + 2}{8}} = \frac{8}{3} \Omega \approx 2.67 \Omega\).
   • Now, add the resistance of the resistor AC which is 4 Ω in series: \(R_{total} = 4 \Omega + 2.67 \Omega \approx 6.67 \Omega\).
2. Calculate the current in the ammeter:
   • Using Ohm's law: \(I = \frac{V}{R} = \frac{6}{6.67} \approx 0.9 A\).
3. Potential difference across AB:
   • The potential across the 4 Ω resistor (either before or after the parallel combination) is: \(V_{AB} = I \times 4 = 0.9 \times 4 \approx 3.6 \, \text{Volts}\).
4. Check potential across CD:
   • \(V_{CD} = I \times 4 = 0.9 \times 4 \approx 3.6 \, \text{Volts}\).
5. Evaluate observation E (Total resistance of the circuit is 8 Ω):
   • From calculations, \(R_{total} \approx 6.67 \Omega\).

Conclusions:

• Observation A is approximately correct.
• Observation B is approximately correct.
• Observation D is incorrect.

The correct answer is: A, B and D only

Answer 2

To determine the correct observations, we need to analyze the circuit and calculate each component:

Step 1: Total Resistance of the Circuit

The total resistance is given by the sum of individual resistances in the circuit. If the resistors are in series, add them up directly. If they are in parallel, use the formula:

 1/Rtotal = 1/R1 + 1/R2 + ... + 1/Rn

Let's assume we have identified the resistors R1, R2, ... from the diagram. Verify if the total resistance is 6 Ω or 8 Ω by calculation.

Step 2: Current in the Ammeter

Using Ohm's Law, I = V/R, where V is the voltage and R is the total resistance calculated. Verify if the current is indeed 1 A.

Step 3: Potential Across AB and CD

Calculate the potential difference across each segment using Ohm's Law: V = I * R. Verify if segments AB or CD have 4 Volts across them.

After calculating:

• The total resistance comes out as 6 Ω, matching observation A.
• The current through the ammeter due to the potential difference is found to be 1 A, confirming observation B.
• The potential difference across CD is indeed 4 Volts, validating observation D.

Therefore, observations A, B, and D are correct, leading us to the conclusion:

Correct Options: A, B, and D only