A circuit is shown in the following figure for which C1=(3±0.011)μF,C2=(5±0.01)μF and C3=(1±0.01)μF.If C is the equivalent capacitance across AB,then C is given by

TS EAMCET · Physics · Current Electricity

A circuit is shown in the following figure for which $C_{1} = (3 \pm 0.011) μ F, C_{2} = (5 \pm 0.01) μ F$ and $C_{3} = (1 \pm 0.01) μ F .$ If $C$ is the equivalent capacitance across $A B,$ then $C$ is given by

A $(0.9 \pm 0.114) μ F$
B $(0.9 \pm 0.01) μ F$
C $(0.9 \pm 0.023) μ F$
D $(0.9 \pm 0.09) μ F$

Verified Solution

Answer & Solution

Correct Answer

(C) $(0.9 \pm 0.023) μ F$

Step-by-step Solution

Detailed explanation

Above circuit with node potential can be drawn as below, Equivalent capacitance of given circuit can be written as,Ceq=3C1C33C1+C3 ⇒Ceq=3C1C33C1+C3 For true value of equivalent capacitance, we have ⇒Ceq=3×3×13×3+1=910=0.9μF For error calculation, we have to use the rule for…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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