(II) A 45-V battery of negligible internal resistance is...

(II) A $45-\mathrm{V}$ battery of negligible internal resistance is connected to a $38-\mathrm{k} \Omega$ and a $27-\mathrm{k} \Omega$ resistor in series. What reading will a voltmeter, of internal resistance 95 $\mathrm{k} \Omega$ , give when used to measure the voltage across each resistor? What is the percent inaccuracy due to meter resistance for each case?

Key Concepts

Series Circuit Analysis

This concept involves understanding how resistors connected in series share the same current and how their total resistance affects the overall voltage drop across the circuit. Analyzing a series circuit requires summing the individual resistances to get the equivalent resistance, which in turn determines the current flow through the circuit using Ohm's law.

Voltage Divider

The voltage divider principle is used to determine the voltage across individual components in a series circuit. It states that the voltage drop across any resistor in a series is proportional to its resistance relative to the total resistance. This rule allows one to calculate expected voltages in ideal conditions, assuming no other elements interfere with the voltage distribution.

Internal Resistance and Loading Effect of a Voltmeter

Real voltmeters have finite internal resistance, which means they draw a small amount of current when connected to a circuit. This effect, known as the loading effect, can alter the voltage distribution being measured, particularly in circuits with high resistance values. Understanding how the internal resistance interacts with the circuit components is crucial for accurately interpreting measurement results.

Percent Error Calculation

This concept involves determining the deviation of a measured or observed value from the true value. In the context of electrical measurements, percent error is calculated by comparing the voltage reading obtained with the voltmeter (affected by its internal resistance) to the ideal voltage drop that would exist without loading. This calculation helps in assessing the accuracy of the measurement instrument.

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