{"id":343705,"date":"2023-01-06T13:33:49","date_gmt":"2023-01-06T08:03:49","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/the-expression-for-the-equivalent-resistance-of-the-combination-of-resistors-r1-r2-and-r3-in-a-series-combination-is__\/"},"modified":"2025-06-30T11:03:04","modified_gmt":"2025-06-30T05:33:04","slug":"the-expression-for-the-equivalent-resistance-of-the-combination-of-resistors-r1-r2-and-r3-in-a-series-combination-is__","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/the-expression-for-the-equivalent-resistance-of-the-combinat\/","title":{"rendered":"The expression for the equivalent resistance of the combination of resistors R1,\u00a0R2 and R3 in a series combination is__"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"The expression for the equivalent resistance of the combination of resistors R1,\u00a0R2 and R3 in a series combination is__","custom_permalink":"question\/physics\/the-expression-for-the-equivalent-resistance-of-the-combinat\/"},"categories":[],"acf":{"question":"

The expression for the equivalent resistance of the combination of resistors <\/span>R<\/mi><\/mrow>1<\/mn><\/mrow><\/msub>,<\/mo> <\/mi>R<\/mi><\/mrow>2<\/mn><\/mrow><\/msub><\/math> <\/span>and <\/span>R<\/mi><\/mrow>3<\/mn><\/mrow><\/msub><\/math> <\/span>in a series combination is__<\/span><\/p>

<\/p>

<\/p><\/spanstyle=\"font-family:'timesnewroman';-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal;font-size:12pt\"><\/spanstyle=\"font-family:'timesnewroman';-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal;font-size:12pt\">","options":[{"option":"R<\/mi><\/mrow>s<\/mi><\/mrow><\/msub>=<\/mo>R<\/mi><\/mrow>1<\/mn><\/mrow><\/msub>+<\/mo>R<\/mi><\/mrow>2<\/mn><\/mrow><\/msub>+<\/mo>R<\/mi><\/mrow>3<\/mn><\/mrow><\/msub><\/math>","correct":true},{"option":"1<\/mn><\/mrow>R<\/mi><\/mrow>s<\/mi><\/mrow><\/msub><\/mrow><\/mfrac>=<\/mo>1<\/mn><\/mrow>R<\/mi><\/mrow>1<\/mn><\/mrow><\/msub><\/mrow><\/mfrac>+<\/mo>1<\/mn><\/mrow>R<\/mi><\/mrow>2<\/mn><\/mrow><\/msub><\/mrow><\/mfrac>+<\/mo>1<\/mn><\/mrow>R<\/mi><\/mrow>3<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><\/math>","correct":false},{"option":"Both 1 and 2<\/span>","correct":false},{"option":"None of the above<\/span> <\/span>","correct":false}],"solution":" <\/span>The expression for the equivalent resistance of the combination of resistors<\/span> R<\/mi><\/mrow>1<\/mn><\/mrow><\/msub>,<\/mo>R<\/mi><\/mrow>2<\/mn><\/mrow><\/msub> and <\/mi>R<\/mi><\/mrow>3<\/mn><\/mrow><\/msub><\/math> <\/span>in a series combination is <\/span>R<\/mi><\/mrow>s<\/mi><\/mrow><\/msub>=<\/mo>R<\/mi><\/mrow>1<\/mn><\/mrow><\/msub>+<\/mo>R<\/mi><\/mrow>2<\/mn><\/mrow><\/msub>+<\/mo>R<\/mi><\/mrow>3<\/mn><\/mrow><\/msub>.<\/mo><\/math>
Given the resistors <\/span>,<\/mo> <\/mi>R<\/mi><\/mrow>1<\/mn><\/mrow><\/msub>,<\/mo> <\/mi>R<\/mi><\/mrow>2<\/mn><\/mrow><\/msub> and <\/mi>R<\/mi><\/mrow>3<\/mn><\/mrow><\/msub><\/math> <\/span>are connected in series with a battery, key, and the ammeter connected. The current I flows through the circuit. The current remains the unchanged in series combination.<\/span>
Let the voltage (potential difference) across each resistance be <\/span>V<\/mi><\/math>.<\/span>
Using Ohm's law we have<\/span>
V<\/mi><\/mrow>1<\/mn><\/mrow><\/msub>=<\/mo>I<\/mi>R<\/mi><\/mrow>1<\/mn><\/mrow><\/msub>;<\/mo> <\/mi>V<\/mi><\/mrow>2<\/mn><\/mrow><\/msub>=<\/mo>I<\/mi>R<\/mi><\/mrow>2<\/mn><\/mrow><\/msub> and <\/mi>V<\/mi><\/mrow>3<\/mn><\/mrow><\/msub>=<\/mo>I<\/mi>R<\/mi><\/mrow>3<\/mn><\/mrow><\/msub><\/math>
Total potential difference across the circuit<\/span> <\/span> <\/span> <\/span>V<\/mi><\/mrow>s<\/mi><\/mrow><\/msub>=<\/mo>V<\/mi><\/mrow>1<\/mn><\/mrow><\/msub>+<\/mo>V<\/mi><\/mrow>2<\/mn><\/mrow><\/msub>+<\/mo>V<\/mi><\/mrow>3<\/mn><\/mrow><\/msub><\/math>
I<\/mi>R<\/mi><\/mrow>s<\/mi><\/mrow><\/msub>=<\/mo>I<\/mi>R<\/mi><\/mrow>1<\/mn><\/mrow><\/msub>+<\/mo>I<\/mi>R<\/mi><\/mrow>2<\/mn><\/mrow><\/msub>+<\/mo>I<\/mi>R<\/mi><\/mrow>3<\/mn><\/mrow><\/msub><\/math>
Therefore <\/span>
R<\/mi><\/mrow>s<\/mi><\/mrow><\/msub>=<\/mo>R<\/mi><\/mrow>1<\/mn><\/mrow><\/msub>+<\/mo>R<\/mi><\/mrow>2<\/mn><\/mrow><\/msub>+<\/mo>R<\/mi><\/mrow>3<\/mn><\/mrow><\/msub><\/math>
Here in a series combination of resistors, the equivalent resistance is equal to the sum of the individual resistances.<\/span>
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