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Combination of Resistors

If the lamps ...

Question

If the lamps are both the same in the fiugre given below and if $A_{1}$ reads 0.50 A, What do $A_{2}, A_{3}, A_{4} a n d A_{5}$ read?

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Solution

Since, both lamps have the same resistance, hence, current divide equally among them, i.e 0.25 A and all the ammeters will show the same current of 0.25 A.

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Q. If the lamps are both the same in the figure given below and if A₁ reads 0.50 A, what do A₂, A₃, A₄ and A₅ read?

a_{1}, a_{2}, a_{3}, a_{4}, a_{5} > 0

\frac{a_{1}}{a_{2} + a_{3}} + \frac{a_{2}}{a_{3} + a_{4}} + \frac{a_{3}}{a_{4} + a_{5}} + \frac{a_{4}}{a_{5} + a_{1}} + \frac{a_{5}}{a_{1} + a_{2}} \geq \frac{5}{2}

a_{1}

a_{2}

a_{3}

a_{2}

a_{3}

a_{4}

a_{3}

a_{4}

a_{5}

a_{1}

a_{3}

a_{5}

a_{1}, a_{2}, a_{3}, a_{4}, a_{5}

are the roots of the equation

6 x^{5} - 41 x^{4} + 97 x^{3} - 97 x^{2} + 41 x - 6 = 0,

| a_{1} | \leq | a_{2} | \leq | a_{3} | \leq | a_{4} | \leq | a_{5} |,

then which of the following is/are correct?

a_{1}, a_{2}, a_{3}

a_{2}, a_{3}, a_{4}

are in G.P., and

a_{3}, a_{4}, a_{5}

are in H.P., then

ln a_{1}, ln a_{3}, ln a_{5}

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