An infinite ladder is constructed with 1 Ω and 2 Ω resistors, as shown in the figure (32-E22). (a) Find the effective resistance between the points A and B. (b) Find the current that passes through the 2 Ω resistor nearest to the battery.
figure 32-E22
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Answer: (a) 2ohm (b) 1.5A
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(a) Between points A and B, the effective resistance is 2 Ω. (b) The current that passes via the 2 Ω resistor nearest to the battery is 1.5 A.
Explanation:
(a) Let R be the combination’s effective resistance. The redrawing of the circuit is displayed below.
It is understood from the figure that
2RR + 2 + 1 = R ⇒3R + 2 = R2 + 2R
⇒R = +1 + 92.1 = 2 Ω
(b) Battery sends the total current which is
6R=62=3 A
62 = 6R = 3A
In loop 1, when Kirchoff’s law is applied, we obtain:
3 × 1 + 2i = 6 ⇒ i =1.5 A
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