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With the switch open, roughly what must be the resistance of the resistor on the right for the current out of the battery to be the same as when the switch is closed (and the resistances of the two resistors are 20 Ω and 10 Ω)?

A) 7ΩB) 15ΩC) 30ΩD) 5Ω

User Saku
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1 Answer

6 votes

Answer:

The resistance must be 6.67
\Omega

Solution:

Resistance,
R_(1) = 20\Omega

Resistance,
R_(2) = 10\Omega

For the current to be the same when the switch is open or closed, the resistances must be connected in parallel as current is distributed in parallel with the same voltage across the circuit:

Thus in parallel:


(1)/(R_(eq)) = (1)/(R_(1)) + (1)/(R_(2))


(1)/(R_(eq)) = (1)/(20) + (1)/(10)


R_(eq) = 6.67\ \Omega

User Mike Fulton
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6.8k points