A direct-current generator has an emf of 120 V ; that is,...

A direct-current generator has an emf of 120 V ; that is, its terminal voltage is 120 V when no current is flowing from it. At an output of 20 A , the terminal potential is 115 V . (a) What is the internal resistance $r$ of the generator? (b) What will be the terminal voltage at an output of 40 A ? The situation is much like that shown in Fig. 26-3. Now, however, $\ell=120 \mathrm{~V}$ and $I$ is no longer 25 A . (a) In this case, $I=20 \mathrm{~A}$ and the p.d. from $A$ to $B$ is 115 V . Therefore, $$ 115 \mathrm{~V}=+120 \mathrm{~V}-(20 \mathrm{~A}) \mathrm{r} $$ from which $r=0.25 \Omega$. (b) Now $I=40 \mathrm{~A}$. So Terminal p.d. $=E-I r=120 \mathrm{~V}-(40 \mathrm{~A})(0.25 \Omega)=110 \mathrm{~V}$ Fig. 26-3

A direct-current generator has an emf of 120 V ; that is, its terminal voltage is 120 V when no current is flowing from it. At an output of 20 A , the terminal potential is 115 V . (a) What is the internal resistance $r$ of the generator? (b) What will be the terminal voltage at an output of 40 A ?

The situation is much like that shown in Fig. 26-3. Now, however, $\ell=120 \mathrm{~V}$ and $I$ is no longer 25 A .
(a) In this case, $I=20 \mathrm{~A}$ and the p.d. from $A$ to $B$ is 115 V . Therefore,

$$
115 \mathrm{~V}=+120 \mathrm{~V}-(20 \mathrm{~A}) \mathrm{r}
$$

from which $r=0.25 \Omega$.
(b) Now $I=40 \mathrm{~A}$. So

Terminal p.d. $=E-I r=120 \mathrm{~V}-(40 \mathrm{~A})(0.25 \Omega)=110 \mathrm{~V}$

Fig. 26-3

Key Concepts

Ohm's Law and Voltage Drop

Ohm's law, which relates voltage, current, and resistance, is used to calculate the voltage drop across the internal resistance of a power source. In a loaded circuit, the terminal voltage can be determined by subtracting the product of the current and the internal resistance (I ? r) from the electromotive force (E), illustrating how increased current draw leads to lower terminal voltage.

Terminal Voltage

Terminal voltage is the actual voltage measured across the output terminals of a power source when it is supplying current. It is lower than the EMF by the amount of voltage dropped across the internal resistance, making it a key indicator of the generator's performance under load.

Electromotive Force (EMF)

Electromotive force is the open-circuit voltage produced by a generator, which represents the maximum potential difference available when no load is connected. It is the fundamental voltage that drives current through a circuit, assuming ideal conditions with no internal losses.

Internal Resistance

Internal resistance is the inherent resistance within a power source, such as a generator, that causes a voltage drop when current flows. It results from the non-ideal materials and structure of the generator and directly affects the output voltage under load conditions by reducing the terminal voltage from its ideal EMF.

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