Question 18.1: Four Resistors in Series Goal Analyze several resistors conn...
Four Resistors in Series
Goal Analyze several resistors connected in series.
Problem Four resistors are arranged as shown in Figure 18.5a. Find (a) the equivalent resistance of the circuit and (b) the current in the circuit if the emf of the battery is 6.0 \mathrm{~V}.
Strategy Because the resistors are connected in series, summing their resistances gives the equivalent resistance. Ohm’s law can then be used to find the current.
(a) Find the equivalent resistance of the circuit.
Apply Equation 18.4,
R_{\mathrm{eq}}=R_{1}+R_{2}+R_{3}+\cdots (18.4)
summing the resistances:
\begin{aligned} R_{\mathrm{eq}} & =R_{1}+R_{2}+R_{3}+R_{4}=2.0 \Omega+4.0 \Omega+5.0 \Omega+7.0 \Omega \\ & =18.0 \Omega \end{aligned}
(b) Find the current in the circuit.
Apply Ohm’s law to the equivalent resistor in Figure 18.5 \mathrm{~b}, solving for the current:
I=\frac{\Delta V}{R_{\mathrm{eq}}}=\frac{6.0 \mathrm{~V}}{18.0 \Omega}=\frac{1}{3} \mathrm{~A}