Question

Four voltmeters are connected to a circuit as shown in figure 16.90. As is usual with voltmeters, the reading on the voltmeter is positive if the negative lead (black wire, usually labled COM) is connected to a location at lower potential, and the positive lead(red) is connected to a location at higher potential. The circuit contains two devices whose identity is unknown and a rod (green) of length 9 cm made of conducting material. At a particular moment, the reading observed in the voltmeters are, voltmeter A: -1.6 V, voltmeter B: -6 V, voltmeter A: -3.5 V. (a) At this moment, what is the reading on voltmeter D, both magnitude and sign? (b) What are the magnitude and direction of the electric field inside the rod?

Short answer

The reading of the voltmeter D is (+) 7.9 V .

Step-by-step solution

Identification of given data

The reading of voltmeter A is V_A = -1.6 V .

The reading of voltmeter B is V_B = -6 V.

The reading of voltmeter C is V_C = -3.5 V .

The length of conducting material is l = 9 cm .

Conceptual Explanation

The Kirchhoff’s voltage law is used to find the reading of the voltmeter D because all the voltmeter is forming a loop.

Determination of reading of voltmeter D

Apply KVL to calculate the reading of voltmeter D.

V_A + V_B - V_c+ V_D = 0

Substitute all the values in the above equation.

- 6 V - 3.5 V - (-1.6 V) + V_D = 0

V_D = 7.9 V

The sign for the magnitude of above reading of voltmeter D is positive.

Therefore, the reading of the voltmeter D is (+) 7.9 V .