### Physics Phun: Current Resistance and Circuits

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

where,

V = potential dropped in the resistor.

## Combination of Resistors:

Series Combination of Resistors:

Here,

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

In Series,

Here,

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)

In Parallel,

Here,

Q = Q1+Q2+Q3

Or, C_eqv*V = C1*V1+C2*V2+C3*V3

C_eqv=  C1+C2+C3                                 (since  V = V1=V2=V3)