1. **Problem statement:** Given a parallel circuit with voltage source $E=20$ V and resistors $R_1=4\ \Omega$, $R_2=6\ \Omega$, $R_3=8\ \Omega$, calculate: (a) Total resistance $R_t$ (b) Total current $I$ (c) Voltage drop across $R_3$, $V_{R3}$ (d) Current through $R_1$, $I_{R1}$ 2. **Formula and rules:** - For resistors in parallel, total resistance is given by: $$\frac{1}{R_t} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$$ - Ohm's law relates voltage, current, and resistance: $$V = IR$$ - In parallel circuits, voltage across each resistor is the same as the source voltage: $$V_{R1} = V_{R2} = V_{R3} = E$$ 3. **Calculate total resistance $R_t$:** $$\frac{1}{R_t} = \frac{1}{4} + \frac{1}{6} + \frac{1}{8}$$ Calculate each term: $$\frac{1}{4} = 0.25, \quad \frac{1}{6} \approx 0.1667, \quad \frac{1}{8} = 0.125$$ Sum: $$0.25 + 0.1667 + 0.125 = 0.5417$$ So: $$R_t = \frac{1}{0.5417} \approx 1.846\ \Omega$$ 4. **Calculate total current $I$ using Ohm's law:** $$I = \frac{E}{R_t} = \frac{20}{1.846} \approx 10.83\ A$$ 5. **Voltage drop across $R_3$:** In parallel circuits, voltage across each resistor equals source voltage: $$V_{R3} = E = 20\ V$$ 6. **Current through $R_1$:** Using Ohm's law: $$I_{R1} = \frac{V_{R1}}{R_1} = \frac{20}{4} = 5\ A$$ **Final answers:** (a) $R_t \approx 1.846\ \Omega$ (b) $I \approx 10.83\ A$ (c) $V_{R3} = 20\ V$ (d) $I_{R1} = 5\ A$