parallelresistanceresistorsseries
A battery of EMF 8.0 V and internal resistance r = 1.0 – is connected to an external circuit as shown:
I need to find out the total resistence and my problem is that I dont know which resistors consider parallel and which are in series as there is connection for 3ohm resistor after 1st resistor which confuses me. Answer I got is that the total resistance is 15ohms could anyone confirm it? Or point out where I went wrong?
In this case I would use Y-delta transformation. As shown in the schematic below:
simulate this circuit – Schematic created using CircuitLab
This should give you one unique solution for an equivalent resistance. It's probably an enormous equation, so luckily you have a CAS.
The equation is basic Ohms Law with parts replaced for power calculation.
The formula is: $$ P=\frac{V^2}{R} $$ As it's got 12V across the resistor, and the resistor measures 51Ω, that becomes: $$ P=\frac{12^2}{51} = 2.82W $$ So you need at least 3W to be safe.
Placing resistors in parallel results in lower resistance. The long form of the formula for that is: $$ \frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + ... + \frac{1}{R_n} $$ So taking three 150Ω resistors in parallel gives you: $$ \frac{1}{R_T} = \frac{1}{150} + \frac{1}{150} + \frac{1}{150} $$ $$ \frac{1}{R_T} = 0.02 $$ $$ R_T = \frac{1}{0.02} = 50\Omega $$ If all the resistors are the same value then it is a simple as dividing the value by the number of resistors, and the power ratings just add together, 20 three 0.5W resistors would give 1.5W of power. Not enough for your application.
If you cannot get 1W resistors then you would be better with six 0.5W resistors of double the value - so 300Ω each.
Best Answer
Start with the part that's easy, and work your way out. 6 ohms in parallel with 12 ohms is 4 ohms. 4 ohms in series with 2 ohms is 6 ohms. 6 ohms in parallel with 3 ohms is 2 ohms. 1 ohm in series with 2 ohms in series with 4 ohms in series with 1 ohm is 8 ohms.