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ICSE Class 10 Physics 2019 Paper

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The diagram above shows a circuit with the key kk open. Calculate :
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Question : 61 of 74
Marks: +1, -0
the resistance of the circuit when the key kk is closed.
Solution:  
When key KK is closed, External Resistance is
;1Rp;=;1(2+3)+;15\\;\frac{1}{R_{p}}\\;=\\;\frac{1}{(2+3)}+\\;\frac{1}{5}
;=;15+;15=;25\\;=\\;\frac{1}{5}+\\;\frac{1}{5}=\\;\frac{2}{5}
∴;;RP=;52=2.5Ω\therefore \\;\\; R_{P}=\\;\frac{5}{2}=2.5\\ \Omega
∴\therefore Total resistance
;=RP+r\\;= R_{P}+r
;=2.5+0.5\\;=2.5+0.5
;=3Ω\\;=3\\ \Omega
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