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| BETA : Direct Current : Resistors 01 : Direct Current Through A Single Resistor - Long Version : BETA Physics Homework Exercise
Description : Direct current through a single resistor - long version (the long version defines all voltages and currents).
Discussion : For a single resistor and ignoring internal resistance, the voltage across the resistor equals the supply voltage, and the current through the resistor equals the supply current. See Figure Direct Current Single Resistor
The homework exercise has 3 sets of questions with 4 questions per set.
Vr, Ir, Is, Pr
Ir, Is, R, Vs
Ir, Vr, Pr, Vs
The basic equations are :
Vr = Vs
Ir = Vr / R
Is = Ir
Pr = Ir Vr = Ir2 R
rearranging
R = Vr / Ir
Vr = R Ir
Ir = Pr / Vr = √(Pr / R)
where
Vs = supply voltage
Vr = voltage across resistor
Is = supply current
Ir = current through resistor
R = resistance
Pr = power through resistor
Current losses through the volt meters and voltage losses across the amp meters are ignored.
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| BETA : Direct Current : Resistors 02 : Direct Current Through A Single Resistor - Short Version : BETA Physics Homework Exercise
Description : Direct current through a single resistor - short version.
Discussion : For a single resistor and ignoring internal resistance, the voltage across the resistor equals the supply voltage, and the current through the resistor equals the supply current. See Figure Direct Current Single Resistor
The homework exercise has 3 sets of questions with 2 questions per set.
I, P
I, V
R, P
The basic equations are :
I = V / R
P = V I = I2 R
rearranging
I = √(P / R)
V = I R
R = V / I
where
V = voltage
I = current
R = resistance
P = power
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| BETA : Direct Current : Resistors 04 : Direct Current Through Two Resistors In Series : BETA Physics Homework Exercise
Description : Direct current through two resistors in series - short version.
Discussion : For two resistors in series the current through both the resistors is the same, and is equal to the supply current. See Figure Direct Current Through Two Resistors In Series
The homework exercise has 3 sets of questions with 7 questions per set.
Re, I, Va, Vb, Pa, Pb, Ps
Va, Vb, Vs, P, Ra, Rb, Re
Vs, I, Ra, Rb, Pa, Pb, Ps
The basic equations are :
Re= Ra + Rb
I = Vs / Re
Va = I Ra
Vb = I Rb
Pa = Va I = I2 Ra
Pb = Vb I = I2 Rb
Ps = Vs I = I2 Re = Pa + Pb
rearranging
Va = Pa / I
Vb = Pb / I
Vs = Va + Vb
Ps = Pa + Pb
Ra = Va / I
Rb = Vb / I
Re = Vs / I
where
I = current
Vs Va Vb = voltage across supply and resistors A and B
Ra Rb = resistors A and B
Re = equivalent resistance of Ra and Rb combined
Ps Pa Pb = power through supply and resistors A and B
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| BETA : Direct Current : Resistors 06 : Direct Current Through Two Resistors In Parallel : BETA Physics Homework Exercise
Description : Direct current through two resistors in parallel - short version.
Discussion : For two resistors in parallel the voltage across both the resistors is the same, and is equal to the supply voltage. See Figure Direct Current Through Two Resistors In Parallel
The homework exercise has 3 sets of questions with 7 questions per set.
Re, V, Ia, Ib, Pa, Pb, Ps
Ia, Ib, Is, Ps, Ra, Rb, Re
Is, V, Ra, Rb, Pa, Pb, Ps
The basic equations are :
Re = (Ra * Rb) / (Ra + Rb) = 1 / (1 / Ra + 1 / Rb)
V = Is * Re
Ia = V / Ra
Ib = V / Rb
Pa = V Ia
Pb = V Ib
Ps = Pa + Pb
rearranging
Ia = Pa / V etc
Is = Ia + Ib
Ps = Pa + Pb
V = Is Re etc
where
Is Ia Ib = current through supply and resistors A and B
V = voltage
Ra Rb = resistors A and B
Re = equivalent resistance of Ra and Rb combined
Ps Pa Pb = power through supply and resistors A and B
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| BETA : Direct Current : Resistors 07 : Direct Current Through One Resistor In Series With Two Resistors In Parallel : BETA Physics Homework Exercise
Description : Direct current through one resistor in series and two resistors in parallel.
Discussion : Two parallel resistors Ra and Rb, are in series with a third resistor Rc. The current through the series resistor is equal to the supply current, and equals the sum of the currents through the parallel resistors. The voltage across the parallel resistors is equal. See Figure Direct Current Through One Series And Two Parallel Resistors
The homework exercise has 3 sets of questions with 6 questions per set.
Re, Ic, Vc, Va, Ia, Ib
Vs, Ib, Rc, Ra, Rb, Re
Ic, Vs, Va, Ia, Ra, Rb
The basic equations are :
Re = (Ra * Rb) / (Ra + Rb) + Rc = 1 / (1 / Ra + 1 / Rb) + Rc
Ic = Vs / Re
Vc = Ic Re
Va = Vs - Vc
Ia = Va / Ra
Ib = Va / Rb
rearranging
Vs = Vc + Va
Ia = Ic - Ib
Ib = Ic - Ia
Ra = Va / Ia
Rb = Va / Ib
Re = Vs / Ic
where
Is Ia Ib Ic = current through supply and resistors A B And C
Vs Va Vc = voltage across supply and resistors A And C (Vb = Va)
Ra Rb Rc = resistors A B And C
Re = equivalent resistance of Ra Rb and Rc combined
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| BETA : Direct Current : Resistors 08 : Direct Current Through Series Resistors In Parallel : BETA Physics Homework Exercise
Description : Direct current through series resistors in parallel.
Discussion : Two sets of resistors in series (Ra and Rb in series) and (Rc and Rd in series) are in parallel. The sum of the current through the parallel resistor pairs is equal to the supply current. The voltage across the parallel resistor pairs is equal to the supply voltage. See Figure Direct Current Through Series Resistors In Parallel
The homework exercise has 3 sets of questions with 8 questions per set.
Re, Is, Ia, Ic, Va, Vb, Vc, Vd
Is, Vs, Vd, Ra, Rb, Rc, Rd, Re
Vs, Vb, Vc, Ia, Ic, Rb, Rc, Rd
The basic equations are :
Re = ((Ra + Rb) (Rc + Rd)) / (Ra + Rb + Rc + Rd) = 1 / (1 / (Ra + Rb) + 1 / (Rc + Rd))
Is = Vs / Re
Ia = Va / (Ra + Rb)
Ic = Vs / (Rc + Rd)
Va = Ia Ra
Vb = Ia Rb (Ib = Ia)
Vc = Ic Rc
Vd = Ic Rd (Id = Ic)
rearranging
Is = Va / Ia etc
Is = Ia + Ic
Ic = Is - Ia
Vs = Va + Vb = Vc + Vd
Ra = Va / Ia
Rb = Vb / Ia (Ib = Ia)
Rc = Vc / Ic
Rd = Vd / Ic (Id = Ic)
where
Is Ia Ic = current through supply and resistors A And C (Ib = Ia And Id = Ic)
Vs Va Vb Vc Vd = voltage across supply and resistors A B C And D
Ra Rb Rc Rd = resistors A B C And D
Re = equivalent resistance of Ra Rb Rc and Rd combined
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| BETA : Direct Current : Resistors 09 : Direct Current Through Parallel Resistors In Series : BETA Physics Homework Exercise
Description : Direct current through parallel resistors in series.
Discussion : Two sets of resistors in parallel (Ra and Rb in parallel) and (Rc and Rd in parallel) are in series. The sum of the voltage across the series resistor pairs is equal to the supply voltage. The current through the parallel resistor pairs is equal to the supply current. See Figure Direct Current Through Parallel Resistors In Series
The homework exercise has 3 sets of questions with 8 questions per set.
Re, Is, Va, Vc, Ia, Ib, Ic, Id
Is, Id, Vs, Ra, Rb, Rc, Rd, Re
Vs, Ia, Ic, Va, Vc, Rb, Rc, Rd
The basic equations are :
Re = (Ra Rb) / (Ra + Rb) + (Rc Rd) / (Rc + Rd) = 1 / (1 / Ra + 1 / Rb) + 1 / (1 / Rc + 1 / Rd)
Is = Vs / Re
Va = Is (Ra + Rb) / (Ra Rb)
Vc = Is * (Rc + Rd) / (Rc Rc)
Ia = Va / Ra
Ib = Va / Rb (Vb = Va)
Ic = Vc / Rc
Id = Vc / Rd (Vd = Vc)
rearranging
Is = Ia + Ib = Ic + Id
Id = Is - Ic
Ia = Is - Ib
Ic = Is - Id
Ra = Va / Ia
Rb = Va / Ib (Vb = Va)
Rd = Vc / Ic
Rd = Vc / Id (Vd = Vc)
Va = Ia Ra
Vs = Va + Vc = Is Re
where
Is Ia Ib Ic Id = current through supply and resistors A B C And D
Vs Va Vc = voltage across supply and resistors A And C (Vb = Va and Vd = Vc)
Ra Rb Rc Rd = resistors A B C And D
Re = equivalent resistance of Ra Rb Rc and Rd combined
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| BETA : Direct Current : Resistors 10 : Direct Current Through Three Resistors In Parallel : BETA Physics Homework Exercise
Description : Direct current through three resistors in parallel.
Discussion : The sum of the current through the resistors is equal to the supply cuurent. The voltage ascross the resistors is equal to the supply voltage. See Figure Direct Current Through Three Parallel Resistors
The homework exercise has 3 sets of questions with 5 questions per set.
Re, Vs, Ia, Ib, Ic
Is, Ra, Rb, Rc, Re
Is, Ia, Ib, Ic, Rc
The basic equations are :
Re = (Ra * Rb * Rc) / ((Ra * Rb) + (Ra * Rc) + (Rb * Rc)) = 1 / (1 / Ra + 1 / Rb + 1 / Rc)
Vs = Is Re
Ia = Vs / Ra
Ib = Vs / Rb
Ic = Vs / Rc
rearranging
Is = Ia + Ib + Ic
Ic = Is - Ia - Ib
Ra = Vs / Ia
Rb = Vs / Ib
Rc = Vs / Ic
Re = Vs / Is
where
Is Ia Ib Ic = current through supply and resistors A B And C
Vs = voltage across supply
Ra Rb Rc = resistors A B And C
Re = equivalent resistance of Ra Rb and Rc combined
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| BETA : Direct Current : Resistors 11 : Direct Current Internal Resistance Of A Battery Or Power Supply : BETA Physics Homework Exercise
Description : Direct current internal resistance of a battery or power supply.
Discussion : The output or supply voltage from a battery or power supply drops as the current increases because of internal resistance. The internal resistance can be modelled as an equivalent resistor in series with the battery or power supply. The open circuit voltage is measured when the circuit is open (eg the switch is open) and zero current is flowing. There is no voltage drop due to internal resistance for an open circuit. The supply current and voltage are measured when the circuit is closed and a current is flowing through the load resistor. See Figure Direct Current Internal Resistance Of A Battery Or Power Supply
The homework exercise has 3 sets of questions with 2 questions per set.
Is, r
Vs, Vo
Vs, R
The basic equations are :
Is = Vs / R
r = (Vo - Vs) / Is
rearranging
Vs = Is R
Vo = Vs + Is r
Vs = Vo = Is r
R = Vs / Is
where
Is = supply current
Vs = supply voltage
R = load resistor
r = internal resistor (equivalent to internal resistance)
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| BETA : Direct Current : Resistors 12 : Direct Current Material Resistance And Resistivity : BETA Physics Homework Exercise
Description : Direct current material resistance and resistivity.
Discussion : The resistance of a resistor is directly proportional to its material resistivity and length, and inversely proportional to its cross section area. Resistivity is a property of the material that the resistor has been made out of. Resistance, cross section area and length are properties of the resistor. See Figure Direct Current Resistance And Resistivity
The homework exercise has 4 sets of questions with 2 questions per set.
R, I
R, rho
R, L
A, V
The basic equations are :
R = rho L / A
I = V / R
rearranging
R = V / I
rho = R A / L
L = R A / rho
A = rho L / R
where
R = resistance
rho = resistivity
L = resistor length
A = resistor cross section area
V = voltage across resistor
I = current through resistor
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| BETA : Direct Current : Resistors 13 : Direct Current Voltage Or Potential Divider : BETA Physics Homework Exercise
Description : Direct current voltage or potential divider - low output resistance.
Discussion : Resistors are often used in electronic components as a cheap method of reducing voltage. A voltage divider or potential divider is formed by two resistors in series across a supply. The reduced voltage is taken from the mid point joining the two resistors. This is an effective method provided that the output or load resistance is much higher than the resistance of the two resistors. When the oputput resistance is high the output voltage is approximately equal to the open circuit output voltage, and can be approximated by the formula :
Vb = Vs Rb / (Ra + Rb)
The difference between the output voltage Vb and the open circuit output voltage Vo gives an indication of how accurately the potential divider is working. When the load resistance is similar in magnitude to the resistance of the two resistors, Vb is very different to Vo. See Figure Direct Current Voltage Or Potential Divider
The homework exercise has 2 sets of questions with 4 questions per set.
Re, Is, Vb, Vo
Vs, Ra, Rb, Rc
The basic equations are :
Re = Ra + Rb Rc / (Rb + Rc)
Is = Vs / Is
Vb = Is Rb Rc / (Rb + Rc)
Vo = Vs Rb / (Ra + Rb)
rearranging
Vs = Is Re
Ra = Re - Vb / Is
Rb = Vo Ra / (Vs - Vo)
Rc = Vb Rb / (Rb Is - Vb)
where
Ra Rb Rc = resistor A B C
Is = supply current
Re = equivalent resistance of resistors A B and C
Vs = supply voltage
Vb = voltage across resistor B
Vo = open circuit voltage across resistor B (measured with zero current through resistor C)
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