There is a voltmeter in a circuit. In order to triple its range, the resistance of how much value should be used?

Options

A. 2R
B. R/2
C. 3R
D. 4R

Explanation

To solve the problem of determining the resistance needed to triple the range of a voltmeter, we can follow these steps:

### Step 1: Understand the Basics
A voltmeter is used to measure the potential difference (voltage) across a component in a circuit. It is connected in parallel with the component whose voltage is being measured.

### Step 2: Define Initial Conditions
Let:
- \( V_1 \) = initial voltage measured by the voltmeter
- \( R \) = internal resistance of the voltmeter
- \( I \) = current flowing through the circuit

According to Ohm's Law, the voltage across the resistor can be expressed as:
\[ V_1 = I \cdot R \]

### Step 3: Define New Conditions
To triple the range of the voltmeter, we need to find the new voltage \( V_2 \):
\[ V_2 = 3V_1 \]

### Step 4: Set Up the New Equation
When we add a new resistance \( R' \) in parallel with the voltmeter, the new voltage can be expressed as:
\[ V_2 = I \cdot R' \]

### Step 5: Substitute for \( V_2 \)
We can substitute \( V_2 \) from the previous step:
\[ 3V_1 = I \cdot R' \]

### Step 6: Substitute for \( V_1 \)
Now, substitute \( V_1 \) from the first equation:
\[ 3(I \cdot R) = I \cdot R' \]

### Step 7: Cancel Out Current
Since current \( I \) is the same in both cases, we can cancel it out (assuming \( I \neq 0 \)):
\[ 3R = R' \]

### Step 8: Conclusion
Thus, the resistance \( R' \) that should be used to triple the range of the voltmeter is:
\[ R' = 3R \]

### Final Answer
The resistance value needed to triple the range of the voltmeter is \( 3R \).

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