Potential Difference Between Two Points — Question 5

Question 5

Loading a divider changes the node voltage through both branch currents

A 12.0 V ideal source drives R1=2.00 kilohm from its positive terminal to M and R2=4.00 kilohm from M to its negative terminal A. A load RL=4.00 kilohm is connected from M to A.

1. Find the loaded midpoint voltage VM-VA and both lower-branch currents.

2. Compare with the unloaded divider voltage and find its fractional decrease.

Question 5 - Solution

Loading a divider changes the node voltage through both branch currents

(a) Method and calculation

$$R_{\mathrm{lower}}=R_2\parallel R_L=\frac{4(4)}{4+4}=2.00\,\mathrm{k\Omega}.$$$$V_M-V_A=12\frac2{2+2}=6.00\,\mathrm V,\quad I_2=I_L=6/4000=1.50\,\mathrm{mA}.$$

(b) Interpretation and further calculation

$$V_{\mathrm{unloaded}}=12\frac4{2+4}=8.00\,\mathrm V.$$$$\frac{V_{\mathrm{unloaded}}-V_{\mathrm{loaded}}}{V_{\mathrm{unloaded}}}=(8-6)/8=.250.$$

Physical check

The top resistor carries the sum of lower-branch currents, so its drop changes when a load is attached.