Units And Measurement

To convert the voltmeter so that it can measure up to 250 V, we use a series resistor. Let the series resistance be , and the total resistance should be such that the voltmeter can measure 250 V when the original meter reads 25 V. Using the formula for voltage division: Where:
- is the new voltage range (250 V),
- is the original maximum voltage (25 V),
- is the resistance of the voltmeter (1000 ). We can rearrange the formula to solve for : Simplifying: Now, solve for : Thus, the required series resistance is .

To determine the dimensional formula for , where is resistance and is capacitance, we start by identifying their individual dimensional formulas. The resistance is given by the formula , where is voltage and is current. The dimensional formula for voltage is and for current is . Therefore, the dimensional formula for resistance is:

Capacitance is given by the formula , where is charge and is voltage. The dimensional formula for charge is , so the dimensional formula for capacitance is:

The product is computed by multiplying the dimensional formulas of and :

Simplifying, we get:

Thus, the correct dimensional formula for simplifies to .