{"id":343805,"date":"2023-01-06T13:37:19","date_gmt":"2023-01-06T08:07:19","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/a-piece-of-wire-of-resistance-r-is-cut-into-five-equal-parts-these-parts-are-then-connected-in-parallel-if-the-equivalent-resistance-of-this-combination-is-r-then-the-ratio-r-r-is\/"},"modified":"2025-06-26T18:19:08","modified_gmt":"2025-06-26T12:49:08","slug":"a-piece-of-wire-of-resistance-r-is-cut-into-five-equal-parts-these-parts-are-then-connected-in-parallel-if-the-equivalent-resistance-of-this-combination-is-r-then-the-ratio-r-r-is","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-piece-of-wire-of-resistance-r-is-cut-into-five-equal-parts\/","title":{"rendered":"A piece of wire of resistance R is cut into five equal parts. These parts are then connected in parallel. If the equivalent resistance of this combination is R’, then the ratio R\/R’ is"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"A piece of wire of resistance R is cut into five equal parts. These parts are then connected in parallel. If the equivalent resistance of this combination is R', then the ratio R\/R' is","custom_permalink":"question\/physics\/a-piece-of-wire-of-resistance-r-is-cut-into-five-equal-parts\/"},"categories":[],"acf":{"question":"

A piece of wire of resistance <\/span>R<\/mi><\/math> is cut into five equal parts. These parts are then connected in parallel. If the equivalent resistance of this combination is <\/span>R<\/mi>'<\/mo><\/math>, then the ratio <\/span>R<\/mi>\/<\/mo>R<\/mi>'<\/mo><\/math> is <\/span><\/p>

<\/p>

<\/p><\/spanstyle=\"font-family:'timesnewroman';-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:115%;font-size:12pt\"><\/spanstyle=\"font-family:'timesnewroman';-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:115%;font-size:12pt\">","options":[{"option":"1<\/mn><\/mrow>25<\/mn><\/mrow><\/mfrac><\/math>","correct":false},{"option":"1<\/mn><\/mrow>5<\/mn><\/mrow><\/mfrac><\/math>","correct":false},{"option":"5<\/mn><\/math>","correct":false},{"option":"25<\/mn><\/math> <\/span>","correct":true}],"solution":"

We are given a piece of wire with resistance R<\/em>, and it is cut into 5 equal parts. The parts are then connected in parallel. The equivalent resistance<\/strong><\/a> of this combination is R'<\/em>, and we are tasked with finding the ratio R\/R'<\/em>.<\/p>\r\n

Step-by-step Solution:<\/strong><\/p>\r\n

1. Wire Resistance (R<\/em>)<\/strong><\/p>\r\n

The wire has an initial resistance denoted by R<\/em>.<\/p>\r\n

2. Cutting the Wire into 5 Equal Parts:<\/strong><\/p>\r\n

When the wire is cut into 5 equal parts, the resistance of each piece becomes R\/5<\/em> because resistance is proportional to length. Since the wire is cut into five equal parts, each part is one-fifth of the original length, which means the resistance of each part is reduced by a factor of 5.<\/p>\r\n

3. Connecting the Pieces in Parallel:<\/strong><\/p>\r\n

When resistors are connected in parallel, the reciprocal of the equivalent resistance (R'<\/em>) is the sum of the reciprocals of the individual resistances. The formula for parallel resistors is:<\/p>\r\n

1\/R' = 1\/R\u2081 + 1\/R\u2082 + ... + 1\/R\u2099<\/p>\r\n

For 5 resistors, each with resistance R\/5<\/em>, the equation becomes:<\/p>\r\n

1\/R' = 1\/(R\/5) + 1\/(R\/5) + 1\/(R\/5) + 1\/(R\/5) + 1\/(R\/5)<\/p>\r\n

Which simplifies to:<\/p>\r\n

1\/R' = 5 × 5\/R = 25\/R<\/p>\r\n

4. Solving for R'<\/em>:<\/strong><\/p>\r\n

Now, we take the reciprocal of both sides to solve for R'<\/em>:<\/p>\r\n

R' = R\/25<\/p>\r\n

5. Finding the Ratio R\/R'<\/em>:<\/strong><\/p>\r\n

The ratio of the original resistance R<\/em> to the equivalent resistance R'<\/em> is:<\/p>\r\n

R\/R' = R\/(R\/25) = 25<\/p>\r\n

Final Answer:<\/strong><\/p>\r\n

The ratio R\/R'<\/em> is 25<\/strong>.<\/p>","subject":""},"yoast_head":"\nA piece of wire of resistance R is cut into five equal parts. These parts are then connected in parallel. If the equivalent resistance of this combination is R', then the ratio R\/R' is - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"A piece of wire of resistance R is cut into five equal parts. These parts are then connected in parallel. 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