Show that the effective capacitance C of a series combination of three capacitors of capactiances `C_1,C_2 and C_3` is given by `C = (C_1C_2C_3)/(C_1C_2+C_3+C_3C_1)`

Derive expression for the total capcitane, when three capacitors of capactiances C_1,C_2 and C_3 are connected in parallel.

Two capacitors of capacitance C_1 and C_2 and joined in series and this combination is joined in parallel with a capacitor of capacitance C_3 find the resultant capacitance.

If C_1,C_2,C_3,C_4 are the coefficients of any four consecutive terms in the expansion of (1+ x)^n , prove that : C_1/(C_1+C_2)+C_3/(C_3+C_4)=(2C_2)/(C_2+C_3) .

Three capacitors of equal capacitance, when connected in series, have a net capacitance of C_1 and when connected in parallel, have a capacitance of C_2 what will be the value of C_1//C_2 ?

Three capacitors C_1, C_2, C_3 are Connected in series. Derive an expression for the equivalent capacitance.

Three capacitors C_1, C_2, C_3 are Connected in series. Derive an expression for the equivalent capacitance.

Find the coefficient of x^4 in the expansion of (1+x)^n (1-x)^n . Deduce that C_2=C_0C_4-C_1C_3+C_2C_2-C_3C_1+ C_4 C_0 .

The question given below consist of an assertion (A) and a reason ( R). Use the following key to choose the appropriate answer to these questions from the codes (a), (b), ( c) and (d) given below: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is NOT the correct explanation of A. (c) A is true but R is false. (d) A is false and R is also false. Assertion: If three capacitors C_1 C_3 . Reason: 1/C_p=1/C_1+1/C_2+1/C_3 .