Question

problem 3
an 8.00 ω resistor and an unknown resistor are connected in series with a 12 v battery. if the
total (equivalent) resistance of the two resistors is 15.9 ω. find
(a) the unknown resistor
(b) the current through each resistor

Explanation:

Step1: Find the unknown resistor

For resistors in series, \(R_{total}=R_1 + R_2\). Let \(R_1 = 8.00\space\Omega\) and \(R_{total}=15.9\space\Omega\). Then \(R_2=R_{total}-R_1\).
\(R_2 = 15.9 - 8.00=7.9\space\Omega\)

Step2: Find the current through each resistor

Using Ohm's law \(I=\frac{V}{R}\). Here \(V = 12\space V\) and \(R = R_{total}=15.9\space\Omega\)
\(I=\frac{12}{15.9}\approx0.755\space A\)

Since in series, current through each resistor is the same.

Answer:

(a) \(7.9\space\Omega\)
(b) \(0.755\space A\)