Find " r "

Electricity and Magnetism Level 2

When the key is opened ,,,

The voltmeter reading is 12V , I=zero

When the key is closed ,,,

The voltmeter reading is 9V , I=1.5A 

      " r " is ..... Ω

" Your answer is only number " for example if your answer is 3 write 3


The answer is 2.

Ahmed Salah by Ahmed Salah , 24, Egypt

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2 solutions

Ahmed Salah
Sep 26, 2014

1 − W h e n t h e k e y i s o p e n e d ; V 1 = 12 V = V B I 1 = 0 A 2 − W h e n t h e k e y i s c l o s e d ; V 2 = 9 V I 2 = 1.5 A A s ; V B = V + I r H e n c e ; V B 1 = V B 2 = V B V B = V B 2 12 = V 2 + I 2 r 12 = 9 + 1.5 r 1.5 r = 12 − 9 1.5 r = 3 r = 3 1.5 r = 2 Ω 1-When\quad the\quad key\quad is\quad opened;\\ { V }_{ 1 }=12V=\boxed { { V }_{ B } } \\ { I }_{ 1 }=0A\\ 2-When\quad the\quad key\quad is\quad closed;\\ { V }_{ 2 }=9V\\ { I }_{ 2 }=1.5A\\ As;\quad \boxed { { V }_{ B }=V+Ir } \\ Hence;\\ { V }_{ B1 }={ V }_{ B2 }=\boxed { { V }_{ B } } \\ { V }_{ B }={ V }_{ B2 }\\ { 12 }={ V }_{ 2 }+{ I }_{ 2 }r\\ 12=9+1.5r\\ 1.5r=12-9\\ 1.5r=3\\ r=\cfrac { 3 }{ 1.5 } \\ \boxed { r=2Ω }

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Krishna Sharma
Sep 25, 2014

You should specify 'r' is internal resistance.

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I think that it is well-known !!!

Ahmed Salah - 6 years, 8 months ago

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