Answer to Question #263509 in Physics for armando

Question

• A 18Ω resistor and a 30Ω resistor are first connected in parallel and then in series with a voltage source of 12V. Find the effective resistance and current in each of the connections of the circuit.

Answer 1

(a) Let's first find the effective resistance in case of the parallel connection of resistors:

$$R_e=\dfrac{R_1R_2}{R_1+R_2}=\dfrac{18\ \Omega\times30\ \Omega}{18\ \Omega+30\ \Omega}=11.25\ \Omega.$$

We can find the current in the circuit as follows:

$$I=\dfrac{V}{R_e}=\dfrac{12\ V}{11.25\ \Omega}=1.1\ A.$$

(b) Let's first find the effective resistance in case of the series connection of resistors:

$$R_e=R_1+R_2=18\ \Omega+30\ \Omega=48\ \Omega.$$

We can find the current in the circuit as follows:

$$I=\dfrac{V}{R_e}=\dfrac{12\ V}{48\ \Omega}=0.25\ A.$$