In an `a.c.` circuit consisting of resistance `R` and inductance `L`, the voltage across `R` is `60` volt and that across `L` is `80` volt.The total voltage across the combination is

Options

A. `140 V`
B. `20 V`
C. `100 V`
D. `70 V`

Answer

To solve the problem, we need to find the total voltage across a combination of resistance (R) and inductance (L) in an AC circuit. The voltages across the resistor (V_R) and the inductor (V_L) are given as follows:

- Voltage across the resistor, \( V_R = 60 \, \text{V} \)
- Voltage across the inductor, \( V_L = 80 \, \text{V} \)

### Step 1: Understand the relationship between voltages in an R-L circuit
In an R-L circuit, the total voltage (V) across the combination is given by the vector sum of the voltages across the resistor and the inductor. This is because the voltages are not in phase; the voltage across the resistor is in phase with the current, while the voltage across the inductor lags the current by 90 degrees.

### Step 2: Use the Pythagorean theorem
The total voltage can be calculated using the Pythagorean theorem:
\[ V = \sqrt{V_R^2 + V_L^2} \]

### Step 3: Substitute the values
Now, we substitute the given values into the equation:
\[ V = \sqrt{(60 \, \text{V})^2 + (80 \, \text{V})^2} \]

### Step 4: Calculate \( V_R^2 \) and \( V_L^2 \)
Calculating the squares:
\[ V_R^2 = 60^2 = 3600 \, \text{V}^2 \]
\[ V_L^2 = 80^2 = 6400 \, \text{V}^2 \]

### Step 5: Add the squares
Now, add these two results:
\[ V_R^2 + V_L^2 = 3600 + 6400 = 10000 \, \text{V}^2 \]

### Step 6: Take the square root
Finally, we take the square root to find the total voltage:
\[ V = \sqrt{10000} = 100 \, \text{V} \]

### Conclusion
The total voltage across the combination of resistance and inductance is:
\[ \boxed{100 \, \text{V}} \]