A potential divider circuit is shown in figure. The output voltage V0 is
- 4V
- 2 mV
- 0.5 V
- 12 mV
The Correct Option is C
Approach Solution - 1
The problem asks to calculate the output voltage \(V_0\) for the given potential divider circuit.
Concept Used:
The circuit shown is a series circuit, and the output voltage is taken across a portion of the total resistance. This is a direct application of the voltage divider rule. The voltage divider formula states that the voltage drop across a resistor (or a combination of resistors) in a series circuit is proportional to its resistance.
The formula is given by:
\[ V_{out} = V_{in} \times \frac{R_{out}}{R_{total}} \]where:
- \(V_{in}\) is the total input voltage from the source.
- \(R_{total}\) is the total equivalent resistance of the series circuit.
- \(R_{out}\) is the resistance across which the output voltage is measured.
Step-by-Step Solution:
Step 1: Identify the given values from the circuit diagram.
The input voltage is \(V_{in} = 4 \, \text{V}\).
The resistors in the series circuit are: \(3.3 \, \text{k}\Omega\) and seven resistors of \(100 \, \Omega\) each.
Step 2: Calculate the total resistance (\(R_{total}\)) of the circuit.
Since all resistors are in series, the total resistance is the sum of all individual resistances. First, convert all resistances to the same unit (Ohms).
\[ 3.3 \, \text{k}\Omega = 3300 \, \Omega \]The total resistance is:
\[ R_{total} = 3300 \, \Omega + (7 \times 100 \, \Omega) \] \[ R_{total} = 3300 \, \Omega + 700 \, \Omega = 4000 \, \Omega \]Step 3: Calculate the resistance (\(R_{out}\)) across which the output voltage \(V_0\) is measured.
From the diagram, the output voltage \(V_0\) is taken across the last five \(100 \, \Omega\) resistors.
\[ R_{out} = 5 \times 100 \, \Omega = 500 \, \Omega \]Step 4: Apply the voltage divider formula to find \(V_0\).
\[ V_0 = V_{in} \times \frac{R_{out}}{R_{total}} \]Substitute the known values into the formula:
\[ V_0 = 4 \, \text{V} \times \frac{500 \, \Omega}{4000 \, \Omega} \]Final Computation & Result:
Simplify the expression to find the final output voltage.
\[ V_0 = 4 \times \frac{500}{4000} \] \[ V_0 = 4 \times \frac{5}{40} = 4 \times \frac{1}{8} \] \[ V_0 = 0.5 \, \text{V} \]The output voltage \(V_0\) is 0.5 V.
Approach Solution -2
Calculate the equivalent resistance \( R_{\text{eq}} \):
\[ R_{\text{eq}} = 4000 \, \Omega \]
Calculate the current:
\[ i = \frac{4}{4000} = \frac{1}{1000} \, \text{A} \]
Then,
\[ V_0 = \frac{1}{1000} \times 500 = 0.5 \, \text{V} \]
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