An ammeter of 5 ohm resistance can read 5 mA . If it is to be used to read 100 volts, how much resistance is to be connected in series

Options

A. `19.9995 Omega`
B. `199.995 Omega`
C. `1999.95 Omega`
D. `19995 Omega`

Answer

To solve the problem of how much resistance needs to be connected in series with an ammeter to convert it into a voltmeter that can read up to 100 volts, we can follow these steps:

### Step 1: Understand the given values
- The resistance of the ammeter (R_a) = 5 ohms
- The maximum current the ammeter can read (I_g) = 5 mA = 5 × 10^(-3) A
- The voltage we want to measure (V) = 100 V

### Step 2: Calculate the total resistance needed for the voltmeter
To convert the ammeter into a voltmeter, we need to find the total resistance (R_total) required to measure 100 V at the maximum current of 5 mA. The relationship between voltage (V), current (I), and resistance (R) is given by Ohm's law:
\[ V = I \times R \]
Rearranging this gives us:
\[ R_{total} = \frac{V}{I} \]

### Step 3: Substitute the known values
Substituting the values we have:
\[ R_{total} = \frac{100 \, \text{V}}{5 \times 10^{-3} \, \text{A}} \]
\[ R_{total} = \frac{100}{0.005} \]
\[ R_{total} = 20000 \, \text{ohms} \]

### Step 4: Calculate the required series resistance
Now, we need to find the resistance (R) that needs to be connected in series with the ammeter. The total resistance (R_total) is the sum of the ammeter's resistance (R_a) and the series resistance (R):
\[ R_{total} = R_a + R \]
Rearranging gives us:
\[ R = R_{total} - R_a \]

### Step 5: Substitute the values
Now substituting the values:
\[ R = 20000 \, \text{ohms} - 5 \, \text{ohms} \]
\[ R = 19995 \, \text{ohms} \]

### Final Answer
The resistance that needs to be connected in series with the ammeter is **19995 ohms**.

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