The motor in a toy car is powered by four batteries in series, which produce a total emf of \(6.00V\). The motor draws \(3.00A\) and develops a \(4.50V\) back emf at normal speed. Each battery has a \(0.100\Omega \) internal resistance. What is the resistance of the motor?

Current is the term used to describe the speed at which charge moves. Resistance is the propensity of a substance to oppose the flow of charge.

\(\begin{array}{c}{I_{back{\rm{ }}}} = 3A\\V = 6V{\rm{ }}\\Back{\rm{ }}emf{\rm{ }} = 4.50\;V\\{r_{{\mathop{\rm int}} {\rm{ }}}} = 0.1\Omega \end{array}\)

The current in a circuit,

\(I = \frac{V}{R},\)

where\(V\)is the potential and\(R\)is the resistance.

First we need find the resistance value,

\(\begin{array}{c}{I_{back{\rm{ }}}} = \frac{{V - {\rm{ }}Back{\rm{ }}emf{\rm{ }}}}{R}\\3 = \frac{{6 - 4.5}}{R}\\R = 0.5\Omega \end{array}\)

The total resistance is\(0.5\Omega \), which is equal to the effective resistance of four batteries and a motor connected in series.

Now we have,

\(\begin{array}{c}{R_{eff{\rm{ }}}} = 4{r_{{\mathop{\rm int}} {\rm{ }}}} + {R_{motor{\rm{ }}}}\\0.5 = 4 \times 0.1 + {R_{motor{\rm{ }}}}\\{R_{motor{\rm{ }}}} = 0.1\Omega \end{array}\)

Therefore, resistance value is \(0.1\Omega \).