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The equivalent resistance, from corner to corner, of 12 resistors connected in a cube is 5/6 that of a single resistor.
Proof:
Start from one corner and flow current through to the opposite corner. You have three resistors. Each of those three resistors is connected to two resistors, in a crisscross pattern. Those six resistors are then connected to three resistors which are connected to the other corner. By symmetry, the voltages at the upper junctions are the same, and then same can be said for the lower junction. You can then simplify the circuit by shorting out the upper junctions and (separately) the lower junctions. This means the circuit is equivalent to three resistors in parallel, in series with six resistors in parallel, in series with three resistors in parallel. This is 1/3 R plus 1/6 R plus 1/3 R, or 5/6 R.
What else can I help you with?
What is the equivalent resistance of three resistor with 3 ohms connected in star?
There is no 'equivalent resistance' for three resistors connected in star.
What is the equivalent resistance of a pair of 8 ohm resistors in series circuit?
Two eight-ohm resistors in series would have a total resistance of 16 ohms. Two eight-ohm resistors in parallel would have a total resistance of four ohms.
How do you find the resistance of a series circuit with n identical resistors?
The total resistance of resistors in series is simply the sum of the resistance values of those resistors. If the resistors are identical, then you can multiply the resistance of one of them by the number of resistors in the circuit.
What is the formula for calculating the equivalent resistance of a series circuit?
Equivalent resistance of a series circuit is the sum of the resistance of all appliances. The formula is R=R1+R2+... where R is equivalent resistance, R1, R2 and so on is the resistance of the individual appliances.
Two resistors of 400 Ohm and 600 Ohm are in parallel What is the equivalent resistance?
Use the general equation for resistance in parallel: 1/R = 1/R1 + 1/R2
Three 8.0-W resistors are connected in series What is their equivalent resistance?
The equivalent resistance of resistors connected in series is simply the sum of their individual resistances. Therefore, the equivalent resistance of three 8.0-W resistors connected in series is 24.0 W.
In what type of circuit will the equivalent resistance be less than the resistors in the circuit?
In a parallel circuit, the equivalent resistance is always less than the resistance of the individual resistors. This occurs because the total current can split across multiple paths, reducing the overall resistance. As more resistors are added in parallel, the equivalent resistance continues to decrease. This behavior contrasts with series circuits, where the equivalent resistance is the sum of all resistors and is always greater than any individual resistor.
What is the relations for the equivalent resistance of a number of resistors connected in series?
Resistance in series is simply the sum of the resistors. RSERIES = SummationI=1,N(RI)
How to find Equivalent resistance when you have both parallel and series resistors?
To find equivalent resistance when you have both parallel and series resistors, start simple and expand... Find the smallest part of the circuit, such as a pair of resistors in series or a pair of resistors in parallel, and compute the equivalent single resistor value. Repeat that process, effectively covering more and more of the circuit, until you arrive at a single resistance that is equivalent to the circuit. For resistors in series: RTOTAL = R1 + R2 For resistors in parallel: RTOTAL = R1R2/(R1+R2)
What is the equivalent resistance of three resistor with 3 ohms connected in star?
There is no 'equivalent resistance' for three resistors connected in star.
What is the equivalent resistance through the entire circuit?
The equivalent resistance is the overall effect all of the resistances in a circuit has. Put another way, it is the value a single resistor in a circuit would have to be in order to have the same effect as all of the resistors resistors combined in a given circuit.
What is the equivalent resistance of a pair of 8 ohm resistors in series circuit?
Two eight-ohm resistors in series would have a total resistance of 16 ohms. Two eight-ohm resistors in parallel would have a total resistance of four ohms.
How do you find the resistance of a series circuit with n identical resistors?
The total resistance of resistors in series is simply the sum of the resistance values of those resistors. If the resistors are identical, then you can multiply the resistance of one of them by the number of resistors in the circuit.
What is the equivalent resistance of a series circuit that has four 5oo ohm resistors?
2000 ohms
If a circuit contains 3-ohm resistance in a series what is the equivalent resistance of combination?
Equation for Equivalent Resistance in Series isReq= R1+R2+R3+...........If each resistor is equal to 3OhmsthenReq= R1+R2+R3Req=3+3+3Req=9 OhmsThe Equivalent resistance is 9 Ohms.
What is the ratio of equivalent resistance of series and parallel combination of n equal resistance to the equivalent resistance on parallel combination?
The ratio of the equivalent resistance of series combination to the parallel combination of n equal resistors is (n^2 - 1)/n.
Which is the total resistance of a circuit that contains twenty 100 ohms resistors connected in parallel?
When resistors of the same value are wired in parallel, the total equivalent resistance (ie the value of one resistor that acts identically to the group of parallel resistors) is equal to the value of the resistors divided by the number of resistors. For example, two 10 ohm resistors in parallel give an equivalent resistance of 10/2=5Ohms. Three 60 ohm resistors in parallel give a total equivalent resistance of 60/3 = 20Ohms. In your case, four 200 Ohm resistors in parallel give 200/4 = 50 Ohms total.
