A circuit consists of a series combination of 6.00-kΩand 5.00-kΩresistors connected across a 50.

step 1 Okay, so here we want to calculate the potential difference across the 5 kilo -oom resistor Whic

A circuit consists of a series combination of 6.00-kΩand...

A circuit consists of a series combination of 6.00-k$\Omega$ and 5.00-k$\Omega$ resistors connected across a 50.0-V battery having negligible internal resistance. You want to measure the true potential difference (that is, the potential difference without the meter present) across the 5.00-k$\Omega$ resistor using a voltmeter having an internal resistance of 10.0 k$\Omega$. (a) What potential difference does the voltmeter measure across the 5.00-k$\Omega$ resistor? (b) What is the $true$ potential difference across this resistor when the meter is not present? (c) By what percentage is the voltmeter reading in error from the true potential difference?

Key Concepts

Measurement Error Calculation

Measurement error in the context of circuit measurements quantifies the difference between the measured value and the true value of a quantity, often expressed as a percentage. Recognizing and calculating this error is important for assessing the accuracy of an instrument and understanding how instrument characteristics, like internal resistance, can impact the readings in practical applications.

Series and Parallel Resistor Combination

In circuit analysis, combining resistors in series or parallel is essential to simplify circuits and calculate equivalent resistance. When an instrument like a voltmeter is connected across a resistor, it forms a parallel connection with that resistor. The effective resistance of the parallel combination is lower than the individual resistances, which in turn affects how the voltage divides among the components.

Voltage Divider

A voltage divider is a fundamental circuit principle used to distribute a voltage across a series of resistors. In a series circuit, the voltage drop across each resistor is proportional to its resistance relative to the overall resistance. This concept helps determine the 'true' potential difference across individual resistors when no other components alter the circuit configuration.

Instrument Loading Effect

Instrument loading refers to the impact that a measuring device, such as a voltmeter, can have on the circuit it is measuring. Real-world measuring instruments do not have infinite resistance; when connected in parallel with a circuit component, their finite internal resistance alters the effective resistance of that branch, thereby modifying the circuit currents and voltages. Understanding this is critical for accurate interpretation of measured values.

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