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ELECTRIC CIRCUITS QUANTITIES 1. VOLTAGE V (V): POTENTIAL DIFFERENCE IN A PARALLEL CIRCUIT: IF YOU WEREN’T GIVEN THE EMF OF THE BATTERY, THEN USE THIS FORMULA: V = TOTAL I × TOTAL R IF YOU WERE GIVEN THE EMF OF THE BATTERY, THEN THE VOLTAGE IS SIMPLY THE SAME AS THE EMF OF THE BATTERY, GIVEN THAT THE COMPONENT IS CONNECTED IN PARALLEL WITH THE BATTERY! (MAKE SURE YOU LOOK AT THE CIRCUIT VERY CAREFULLY, AS THIS CAN BE VERY TRICKY). IF IT’S NOT CONNECTED TO THE BATTERY DIRECTLY, THEN YOU WILL SIMPLY USE THE FORMULA: p.d. = SPECIFIC I × SPECIFIC R SO FOR EXAMPLE: In this circuit, the p.d. across the 3Ω resistor is 12V, as the 3Ω resistor is connected to the battery directly, meaning it’s in parallel with the battery, therefore, it has the same p.d. across it as the EMF of the battery which is 12V. In this circuit however, the p.d. across the 2Ω resistor is NOT 6V like the EMF of the battery, as the 2Ω resistor is not connected to the battery directly (as there is a resistor on the right hand side), meaning it’s in series with the battery, and therefore, the p.d. across it is NOT the same as the EMF of the battery. POTENTIAL DIFFERENCE IN A SERIES CIRCUIT: IF YOU WEREN’T GIVEN THE EMF OF THE BATTERY / IF YOU WERE GIVEN THE EMF OF THE BATTERY AND YOUR COMPONENT IS NOT CONNECTED DIRECTLY TO YOUR BATTERY, i.e. CONNECTED IN SERIES WITH THE BATTERY, USE THIS FORMULA: V = TOTAL / SPECIFIC I (AS YOU CAN HAVE A PARALLEL CIRCUIT IN A SERIES CIRCUIT) × SPECIFIC R (RESISTANCE OF THIS CERTAIN COMPONENT THAT YOU ARE TRYING TO FIND THE p.d. ACROSS IT) If you were asked to find the p.d. between the terminals X and Y in this circuit, the p.d. in the strands of wire above and below terminals X and Y would be the same as it’s a parallel circuit (JUST THE BIT BETWEEN TERMINALS X AND Y). To get the p.d. in the series circuit which is the strand of wire above terminals X and Y, you will have to simply multiply the total current (that was given in the question as the reading of the ammeter) by the specific resistance 3Ω. This p.d. will be same in the series circuit that’s below terminals X and Y, as the two series circuits above and below terminals X and Y are in parallel. IF YOU WERE GIVEN THE EMF OF THE BATTERY, THEN SIMPLY, THE EMF OF THE BATTERY IS SPLIT BETWEEN THE COMPONENTS, WITH THE ONE THAT HAS THE HIGHEST Ω WILL GET THE HIGHEST V. TO CALCULATE HOW MUCH EACH COMPONENT RECEIVES, USE RATIOS!!! BE AWARE OF THIS POINT: IF THERE WERE FOR EXAMPLE 2 RESISTORS, YOU CAN GET THE p.d. ACROSS ONE OF THEM AND THEN SUBTRACT THIS p.d. FROM THE TOTAL EMF OF THE BATTERY, TO GET THE p.d. ACROSS THE OTHER ONE. 2. RESISTANCE R (Ω): TOTAL / EFFECTIVE RESISTANCE OF RESISTORS IN SERIES: RT or Rp = R1 + R2 + R3 + R4 + ………………………………. TOTAL / EFFECTIVE RESISTANCE OF RESISTORS IN PARALLEL: (TOTAL RESISTANCE WILL LESS THAN THE RESISTANCE OF THE LEAST RESISTOR): 2 RESISTORS IN PARALLEL: RT or Rp = (R1×R2) / (R1+R2) 3 OR MORE RESISTORS IN PARALLEL: RT or Rp = RECIPROCAL OF (1/R1 + 1/R2 + 1/R3 + ………..) IF YOU ADD MORE RESISTORS IN PARALLEL, THE TOTAL Ω DECREASES. IN A PARALLEL CIRCUIT, IF YOU ADD IDENTICAL RESISTORS IN PARALLEL, THEY WILL HAVE THE SAME CURRENT AND SAME VOLTAGE ACROSS THEM AS THEY HAVE THE SAME Ω. Be careful in this circuit while finding the combined resistance, R, of the resistors. Firstly, find the R of the resistors which are together. That would be the total R of the resistors in parallel, the 1Ω and the 3Ω resistor. Then add the total R of these resistors to the resistor in series, which is the 2Ω resistor. RESISTOR(S) IN A SERIES CIRCUIT: Voltage (leftover) / Total Current RESISTOR(S) IN A PARALLEL CIRCUIT: Total EMF of the battery / Specific (TOTAL) current flowing in through it (them) in this strand of wire 3. CURRENT I (A): CURRENT IN A SERIES CIRCUIT: I = TOTAL EMF / TOTAL R CURRENT IN A PARALLEL CIRCUIT/ IF COMPONENT IS CONNECTED TO THE BATTERY DIRECTLY: TOTAL CURRENT (I1) = SUM OF ALL SPECIFIC CURRENTS OR EMF / TOTAL Ω SPECIFIC CURRENT = P.D (USUALLY EMF, HOWEVER, IT WILL NOT BE EMF IF THE COMPONENT IS NOT CONNECTED DIRECTLY TO THE BATTERY, FOR EXAMPLE IF THERE IS A RESISTOR ON THE SIDE, IN WHICH CASE YOU WILL HAVE TO USE THE FORMULA SPECIFIC CURRENT × VOLTAGE LEFT OVER FROM THE VOLTAGE TAKEN BY THE RESISTOR WHICH WILL BE THE SAME ACROSS THE OTHER PARALLEL STRANDS OF WIRE) / SPECIFIC R (RESISTANCE OF THIS CERTAIN COMPONENT (S) THAT YOU ARE TRYING TO FIND THE CURRENT FLOWING THROUGH IT / THEM) MAKE SURE YOU KNOW THE RELATIONSHIPS BETWEEN CURRENTS IN AN ELECTRIC CIRCUIT For example in this circuit, relationships would be: I1 = 14 I2 + I3 = I4