A circuit has three resistances connected in parallel. The voltage sources gives 100 volts. ...?

Question

A circuit has three resistances connected in parallel. The voltage sources gives 100 volts. The current through each resistance is equal to 2 amperes.
Find the value of each resistance.
Find the total current.
Find the effective resistance of the circuit.

What is the total effective resistance of a series network made up of two 75 ohm resistances? Does the order in which these resistance are connected make any difference?

Answer 1

When resistors pass the same current in a parallel curcuit they have the same resistance as they all see the same voltage. Since each resistor is passing 2 amps at 100 volts the resistance must be 50 ohms.

100v/2amps = 50 ohms

Since there are 3 in parallel and each one passes 2 amps the total current must be 6 amps. The effective resistance would be:

100volts/6amps = 16.67 ohms.

or another way: 50ohms/3 = 16.67ohms

Important: the second equation only holds for parallel circuits wher all the resistances are the same!

The more general rule to solve these is by taking the reciprocal of the individual resistances, adding them and then taking the reciprocal of the sum. This works even when the resistances are not the same value.

1/(1/50 + 1/50 + 1/50) = 16.67 ohms

For the second part, when you have resistors in series, you just add up the values, so two 75 ohm resistors in series would be: 75 + 75 = 150 ohms.

Answer 2

Since current flowing in the three resistors is same when connected in parallel, hence each resistor is of the same value ( say r ohm).

Let us now consider one resistor (r ohm). It has been connectd across 100 Volts. and the current through it is 2 amp. Therefore according to Ohm's law -

E = Ir, ie voltage = Current x resistance
ie r = E/I = 100/2 = 50 ohm .

Hence each resistance (r) is of 50 ohm ............ Answer

Total current = 2 + 2 + 2 = 6 amp.............. Answer

Effective resistance of the circuit (R) may be calculated from the formula -

1 / R = 1/r + 1/r + 1/r
= 3 / r = 3 / 50

Hence the required Resistance = 50/3 ohm.
= 16 . 66 (recurring) ohm .................. Answer

Answer 3

The category you picked is likely best for getting correct information. The risk of early LED failure with 91 ohm resistors is tiny. 1/8 th watt resistors should be very reliable. The 4 inch globe will get warm. The 6 inch may not even be noticeably warm. I personally would not use my USB port for experimental circuits, but the risk is tiny. If the 5 volt adaptor is rated more than150 milliamps, it will likely supply your LEDs with a bit more than 5 volts, which does put your LEDs at risk for early failure. Even a 4.5 volt adaptor rated more than 250 milliamps will possibly endanger your LEDs with 91 ohm resistors. Even 110 ohm resistors are a risk with some kinds of 5 volt adapters.Three energizers, or alkaline rechargeable cells or four 1.2 volt cells are safer. Yes equal values of resistors on parallel add for wattage, but they divide for resistance, so bundling two 200 ohm resistors in parallel will give you 100 ohms. I didn't look at the web site, so I can't comment. I have operated similar LEDs in parallel with two 1.5 volt cells (and no resistor) with good luck, but perhaps I have been lucky. Neil