Question

1. What is the equivalent resistance in this circuit?
2. What is the current in this circuit?

Answer 1

1. The equivalent resistance in a series circuit, like the one shown, is given by the general equation

`R_(S) = R_1 + R_2 + R_3 + . . . + R_(N-1) + R_N = \sum_(i=1)^N R_i`

where N is the number of resistors in series. Here, there are four resistors in series. Using our equation with N = 4, we obtain

`R_(S) &= R_1 + R_2 + R_3 + R_4 \\ R_(S) = 2.0 \, \Omega + 3.0 \, \Omega + 4.0 \, \Omega + 6.0 \, \Omega \\ R_(S) = 15.0 \, \Omega.`

2. The current in this series circuit is equal to the voltage divided by the equivalent resistance (a relationship you can derive from Ohm's law):

`I = (V)/(R_(S)) = (45 \, V)/(15.0 \, \Omega) = 3.0 \, A. \\onumber`