All Problems

Electric Current

Problem 3.179

Fig. 3.43 illustrates a potentiometric circuit by means of which we can vary a voltage VV applied to a certain device possessing a resistance R.R . The potentiometer has a length ll and a resistance R0,R_{0}, and voltage V0V_{0} is applied to its terminals. Find the voltage VV fed to the device as a function of distance xx. Analyse separately the case RR0R \gg R_{0}.

Reveal Answer
 3.179. V=V0Rx/[Rl+R0(lx)x/l]; for RR0VV0x/l\begin{aligned} &\text { 3.179. } V=V_{0} R x /\left[R l+R_{0}(l-x) x / l\right] ; \quad \text { for } \quad R \gg R_{0} \quad V \approx\\ &\approx V_{0} x / l \end{aligned}