When studying the physics of currents, circuits and resistors, it is good to know what these terms mean.
Current: The rate of flow of charge.
Ø The electrical field developed due to potential difference in a wire drives the current in the wire.
Ø The current leaving a resistor* is exactly same as entering to it.
Resistor: Any component in a circuit that resists the flow of current through it is called a resistor.
Resistance: The property of material that resists the flow of charge is known as resistance.
Resistance of a material ® is proportional to l/A
And actually R = d*(l/A) where,
l = length of material
A = cross-sectional area
d = resistivity of the material
- 1/d = K = conductivity of a material.
Ohm’s Law: The current flowing in a wire is directly proportional to the potential difference applied to it.
i.e. I is proportional to V
So that I = (1/R)*V ⇒ V = IR
where, 1/R is a proportionality constant.
Power: The energy used by the resistors is supplied by the emf of a battery.
Power supplied by the battery (P_emf) = I*E
Power dissipated by resistors (P_R) = I*V = (I^2)*R
V = potential dropped in the resistor.
Combination of Resistors:
Series Combination of Resistors:
V = V1+ V2 + V3
Or, IR = IR1 + IR2 + IR3 (Since I is constant everywhere in this circuit)
Thus R_eqv.= R1+R2+R3, the “effective” resistance of the 3 put together
Parallel Combination of Resistors:
Here the current is split up into 3 paths, but the voltage across each resistor is constant
I = I1+I2+I3 V=V1+V2+V3
Or, V/R = V1/R1+V2/R2+V3/R3
Thus 1/R_eqv= 1/R1 + 1/R2 + 1/R
Kirchoff’s Voltage Law (KVL):
For a closed loop,
V = V1+V2+V3
∴ V – IR1 – IR2 – IR3= 0
Kirchoff’s Current Law (KCL):
At a junction,
Total current into a region= total current out of the region
So I =I1+I2+I3
Combination of Capacitors:
C = (ε*A)/d ; e= electric permittivity of material inside capacitor, A= Area of capacitor plates, and d= distance between the capacitor plates
- Charge accumulated by a capacitor is (Q) = CV
V = V1+V2+V3
Or, Q/C = Q1/C1+Q2/C2+Q3/C3
Thus 1/C_eqv= 1/C1+ 1/C2+ 1/C3 (since Q = Q1 = Q2 = Q3)
Q = Q1+Q2+Q3
Or, C_eqv*V = C1*V1+C2*V2+C3*V3
C_eqv= C1+C2+C3 (since V = V1=V2=V3)