Crack the Problem

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Find the equivalent capacitance CAB of the circuit as shown in the figure. Submission: Closed Answer: 2C

Cracked by: Yash Agrawal, Bhopal (M.P.). Tushar Jain, Meerut U.P. Rohan Bharadwaj, XIIth, Indian High School, Dubai. Jathin Das, Class XII, Abu Dhabi Indian School, Abu Dhabi, UAE. Gaurav Mathur, XIIth, Maheshwari Sr. Secondary School, Jodhpur.

(19) If z₁,z₂ and z₃ are three points on a circle | z | = r, r > 0, prove that the point of intersection of the chord joining z₁ and z₂ and the tangent at z₃ is .

Submission: Closed

Cracked by:

Swapneel Subhash Sonawane, 11^th, D. G. Ruparel College, Mumbai, X marks 93.46%

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(17) The freshness of the fish can be measured by placing a fish between the plates of a capacitor and measuring the capacitance. How does this work?

Submission: Closed

Cracked by:

Nikhil Dani, Campion School, Bhopal (M.P.).

Here is the answer provided by him:

The capacitance of any capacitor depends on three factors, the overlapping area, the distance between the plates and the dielectric constant of the space in which it is kept . To have an idea about the freshness of the fish, take a capacitor and measure its capacitance. Now, place a fish between its plates. As the fish loses its moisture, the dielectric constant will change. Since all other parameters are constants, we can conclude that the capacitance will be related only to the dielectric constant, or only to the moisture contained, which itself is related to the moisture lost. Hence, knowing the kinetics of losing moisture (zero order, first order, second order etc.) we can easily relate the capacitance and the time.

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