Question

Find the voltage drop between points A and B in the circuit. [?] V 106 A 30 Ω 40 Ω B 50 Ω 20Ω 10Ω​

Answer 1

`30 \Omega || 40\Omega ~ \text{and}~50\Omega || 30 \Omega\\\\\text{Equivalent resistance of the whole circuit,}\\ \\R_(eq) = \left((30 * 40)/(30+40) \right) + \left( (50 * 30)/(50+30) \right)\\\\\\~~~~~~=(1005)/(28)~ \Omega\\\\\text{By Ohm's law,}\\\\~~~~~V=IR\\\\\implies I = (V)/(R) = \frac{9}{\tfrac{1005}{28}} = (252)/(1005)= (84)/(335)~ A\\\\ \text{Voltage drop between points A and B,}\\\\V_(AB) = IR_(AB)\\\\\\`

`~~~~~~~=(84)/(335) \cdot \left((30 * 40)/(30+40) \right)\\\\\\~~~~~~~= \left( (84)/(335) \right) \left(\frac{120} 7 \right)\\\\\\~~~~~~~=(288)/(67)~V\\\\\\~~~~~~~=4.298~V`