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Exercise:
Two RO resistors are connected in series to a voltage supply with VO. A voltmeter with a resistance of RMO is used to measure the partial voltage across one of the resistors. What does it read?

Solution:
The voltmeter resistance sscRM is connected in parallel to one of the two series resistors R. The equivalent resistance for the two parallel resistors is given by sscRp leftfracR+fracsscRMright^- fracRsscRMR+sscRM The partial voltage across the parallel resistors and therefore the voltage measured by the voltmeter is given by fracsscDelta VMsscDelta Vtot fracsscRpsscRp+R fracfracRsscRMR+sscRMfracRsscRMR+sscRM+R fracRsscRMRR+sscRM+RsscRM fracRsscRMR^+ RsscRM Solving for the voltage sscVM leads to sscVM VMF VtimesfracRtimesRMR^+timesRtimesRM VM approx resultVMP
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Exercise:
Two RO resistors are connected in series to a voltage supply with VO. A voltmeter with a resistance of RMO is used to measure the partial voltage across one of the resistors. What does it read?

Solution:
The voltmeter resistance sscRM is connected in parallel to one of the two series resistors R. The equivalent resistance for the two parallel resistors is given by sscRp leftfracR+fracsscRMright^- fracRsscRMR+sscRM The partial voltage across the parallel resistors and therefore the voltage measured by the voltmeter is given by fracsscDelta VMsscDelta Vtot fracsscRpsscRp+R fracfracRsscRMR+sscRMfracRsscRMR+sscRM+R fracRsscRMRR+sscRM+RsscRM fracRsscRMR^+ RsscRM Solving for the voltage sscVM leads to sscVM VMF VtimesfracRtimesRMR^+timesRtimesRM VM approx resultVMP
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Attributes & Decorations
Branches
Direct Current
Tags
resistor, resistor circuit, series resistors, voltmeter
Content image
Difficulty
(3, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
Creator by
Decoration
File
Link