Each element in the finite chain of resistors shown in the figure is 1 Ω. A current of 1 A flows through the final element. The potential difference V across the input terminals of the chain is (30 + n) volt. Find n

Question

Each element in the finite chain of resistors shown in the figure is 1 Ω. A current of 1 A flows through the final element. The potential difference V across the input terminals of the chain is (30 + n) volt. Find n <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-gksuh7mwfwwadnmr.jpg" /> (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Number the resistors, starting with the last element in the chain. As current of

1 A

flows through the first resistor, a current of

1 A

has to flow through the second one as well, thus there is a potential different

(p . d)

of

1 V

across each resistor. As a consequence, the

p . d .

across the third resistor is

(1 + 1) = 2 V,

and the current flowing through it must be

2 A

. The current flowing through the next resistor is

(1 + 2)

= 3 A .

The current in the fifth resistor can be determined using the

p . d .

(2 + 3) = 5 V

across the resistors with currents of

2

and

3 A

, respectively, flowing through them and so on, as shown in figure.
Solution

Q. Each element in the finite chain of resistors shown in the figure is 1Ω. A current of 1A flows through the final element. The potential difference V across the input terminals of the chain is (30+n) volt. Find n

Q. Each element in the finite chain of resistors shown in the figure is $1 Ω.$ A current of $1 A$ flows through the final element. The potential difference $V$ across the input terminals of the chain is $(30 + n)$ volt. Find $n$