Four resistors R\(_1\),R\(_2\),R\(_3\), and R\(_4\) are connected in series as shown above, V\(_1\),V\(_2\),V\(_3\) are voltmeters connected as indicated above. Which of the following relations is correct??
Attached Figure / Diagram
A
V1 = V3 =V2/2
B
V1 = 2V2 = V3
C
V1=1/2V3 =V3
D
V2 - V1 = V3
Verified Correct Answer: A.
Physical Principles & Numerical Solution
From the diagram: The four resistors (\(R_1, R_2, R_3, R_4\)) are in series, so the same current (I) flows through all of them.
The voltmeters are connected as follows:
Voltmeter
Measures the voltage across
\(V_1\)
\(R_1\)
\(V_2\)
\(R_2 + R_3\)
\(V_3\)
\(R_4\)
Using Ohm’s Law:
V = IR
So, \(V_1 = IR_1\)
\(V_2 = I(R_2 + R_3)\)
\(V_3 = IR_4\)
In this type of question, the resistors are usually assumed equal:
\(R_1 = R_2 = R_3 = R_4\) = R
Calculate the voltages
\(V_1\) = IR
\(V_2\) = I(R + R) = 2IR
\(V_3\) = IR
Compare them
\(V_1 = V_3\)
and \(V_2 = 2V_1\)
]Therefore: \(V_1 = V_3 = \frac{V_2}{2}\)
Source: Myschool Past Questions Archive (Record #41637)