Question

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

Answer 1

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:

$\frac{1}{R_{eq}} = \frac{1}{R_{1}} + \frac{1}{R_{2}}$

$\frac{1}{R_{eq}} = \frac{1}{20} + \frac{1}{10}$

$R_{eq} = 6.67\ \Omega$