Voltmeters `V_(1)` and `V_(2)` are connected in series across a `D.C.` line `V_(1)` reads 80 volts and has a per volt resistance of `200 ohms`, `V_(2)` has a total resistance of 32 kilo ohms.
The line voltage is

Options

A. 120 V
B. 160 V
C. 220 V
D. 240 V

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Determine the resistance of voltmeter V1
The resistance of voltmeter V1 can be calculated using its per volt resistance and the voltage it reads.

\[ R_1 = V_1 \times \text{(per volt resistance of V1)} = 80 \, \text{volts} \times 200 \, \text{ohms/volt} = 16,000 \, \text{ohms} = 16 \, \text{kilo ohms} \]

### Step 2: Identify the resistance of voltmeter V2
The total resistance of voltmeter V2 is given directly in the problem.

\[ R_2 = 32 \, \text{kilo ohms} \]

### Step 3: Calculate the equivalent resistance of the series combination
Since the voltmeters are connected in series, the total or equivalent resistance \( R_{eq} \) can be calculated by adding the individual resistances.

\[ R_{eq} = R_1 + R_2 = 16 \, \text{kilo ohms} + 32 \, \text{kilo ohms} = 48 \, \text{kilo ohms} \]

### Step 4: Use Ohm's Law to find the line voltage
According to Ohm's Law, the current \( I \) flowing through the circuit can be expressed as:

\[ I = \frac{V}{R_{eq}} \]

Where \( V \) is the line voltage. The current through V1 can also be expressed as:

\[ I = \frac{V_1}{R_1} \]

Setting these two expressions for current equal to each other gives:

\[ \frac{V}{R_{eq}} = \frac{V_1}{R_1} \]

Rearranging this equation to solve for \( V \):

\[ V = V_1 \times \frac{R_{eq}}{R_1} \]

### Step 5: Substitute the known values
Substituting the known values into the equation:

\[ V = 80 \, \text{volts} \times \frac{48 \, \text{kilo ohms}}{16 \, \text{kilo ohms}} = 80 \, \text{volts} \times 3 = 240 \, \text{volts} \]

### Final Answer
The line voltage is \( 240 \, \text{volts} \).

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