# How to use voltage division for series-parallel circuit

We know that: A voltage divider is a simple circuit which turns a large voltage into a smaller one. Using just two series resistors and an input voltage, we can create an output voltage that is a fraction of the input.

But I am unable to figure out $$\V_x\$$ across the 6 ohm resistor.

The 12 and 6 ohm resistors in parallel threw me off.

• $\Large V_X = V_C * \frac{12\Omega || 6\Omega }{(12\Omega || 6\Omega ) + 8\Omega} = V_C * \frac{\frac{12\Omega}{3}}{ \frac{12\Omega}{3} + 8\Omega } = V_C * \frac{4\Omega }{4 + 8\Omega} = V_C * \frac{4\Omega}{12\Omega}$ – G36 Jun 20 '19 at 6:23
• What you should do is calculate the equivalent resistance of 12 ohms and 6 ohms in parallel, which happens to be 4 ohms, and substitute that in the schematic. G36's comment here shows how to do this. – Bart Jun 20 '19 at 6:50
• Just curious. Why was the value for the capacitor provided, unless you have an exponential decay taking place that you need to address in the answer? – jonk Jun 20 '19 at 6:53
• Thanks y'all I think I understand now – Mattizzy Jun 20 '19 at 13:58
• Yes I am calculating the exponential decay @jonk – Mattizzy Jun 22 '19 at 1:13

Since the 12 ohm and 6 ohm resistors are in parallel, the voltage across both of them is the same $$\V_x\$$ Volts. So you can find out the equivalent resistance as $$\R_{eq} = 12||6 = \frac{12*6}{12+6} = 4\$$. So now, you have a 4 ohm resistor in series with a 8 ohm resistor. Using voltage division, you get $$\V_x = V_c * \frac{4}{4+8} = \frac{V_c}{3}\$$.
• I don't want to be a little off but I was thinking that since 6 ohm and 12 ohm are in series I was thinking we can just apply voltage division right away like$V_x = V_c * \frac{6}{6+12} = \frac{V_c}{3}$ – Mattizzy Jun 25 '19 at 2:37
• But then what about the 8 ohm resistor. Since even that is connected in series it has an affect. The circuit can be considered as a 8 ohm is series with 12 ohm = 20 ohm resistor. After this you can use voltage division and you get $V_x = V_c * \frac{6}{6+20} = \frac{3*V_c}{13}$ – Prateek Dhanuka Jun 25 '19 at 4:37