Complex current

Electricity and Magnetism Level 3

The network shown in the figure above consists of four identical batteries and 11 unknown resistors. When an ideal ammeter is connected between the terminals A and B, its reading is 2 A and when a resistance of $2 \Omega$ is connected in series with the ammeter its reading becomes $1 \text{ A}$ . Now the ammeter and the resistance are disconnected and an ideal voltmeter is connected between the terminals A and B. What would the voltmeter read?

The answer is 4.

1 solution

Chew-Seong Cheong
Jan 20, 2017

By Thévenin's theorem , any circuit of voltage sources and resistors with two terminals can be transformed into an equivalent circuit of a voltage source and a resistance (see left figure above). From the equivalent circuits above, we have:

$\begin{cases} \dfrac {V_{Th}}{R_{Th}} = 2 & \implies V_{Th} = 2 R_{Th} & ...(1) \\ \dfrac {V_{Th}}{R_{Th}+2} = 1 & \implies V_{Th} = R_{Th} + 2 & ...(2) \end{cases}$

$\begin{aligned} (1) = (2): \quad 2 R_{Th} & = R_{Th} + 2 \\ \implies R_{Th} & = 2 \ \Omega \\ (1): \qquad \qquad V_{Th} & = 2R_{Th} \\ & = \boxed{4} \text{ V}\end{aligned}$

THank u sir

avi solanki - 4 years, 4 months ago

In the future you should cut out the picture and paste, and type the text. When you cut out the picture, you should leave small side margins so that the picture looks big enough. I have done that for you in this problem.

Chew-Seong Cheong - 4 years, 4 months ago

yes i will .thanks :)

avi solanki - 4 years, 4 months ago

Complex current

The answer is 4.

1 solution

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