Laws of Indices
Used to simplify expressions involving exponents or powers. Some key points to consider include:
• In an expression with a base and an index or power, the base represents the number being
multiplied by itself and the index represents the number of times the base is being multiplied by
itself.
• The first law of indices states that when expressions with the same base are multiplied, the indices
are added.
• The second law of indices states that when an expression with a base is raised to a power, the index
of the resulting expression is the product of the base and the power.
• The third law of indices states that when expressions with the same index are divided, the indices
are subtracted.
• The fourth law of indices states that when an expression with a power is raised to another power,
the indices are multiplied.
• The use of indices can help to simplify expressions and make calculations easier, particularly when
dealing with large or complex numbers.
Power Dissipation in a Resistor
• The power, P, dissipated in a resistor is given by the formula P = I^2 * R, where I is the current
flowing through the resistor and R is the resistance value. P is measured in watts, I is measured in
amps, and R is measured in ohms.
• There is an alternative formula for power dissipation in a resistor that uses the voltage, V, across the
resistor. Using Ohm's law, we can derive the formula P = V^2 / R.
• When dividing expressions involving indices, we subtract the indices if the bases are the same.
• Negative indices can be interpreted by inverting the expression and changing the sign of the index.
For example, a^-m = 1/a^m.
• To simplify expressions with negative indices, we can rewrite them using positive indices by
inverting the expression and changing the sign of the index.
• We can use the laws of indices to simplify expressions involving powers of numbers or variables.
Resistors in parallel
• Resistors in parallel are a common arrangement in electrical circuits where two or more resistors
are connected across the same voltage source terminals.
• Figure 1.1 shows two resistors R1 and R2 connected in parallel with a voltage source.
Used to simplify expressions involving exponents or powers. Some key points to consider include:
• In an expression with a base and an index or power, the base represents the number being
multiplied by itself and the index represents the number of times the base is being multiplied by
itself.
• The first law of indices states that when expressions with the same base are multiplied, the indices
are added.
• The second law of indices states that when an expression with a base is raised to a power, the index
of the resulting expression is the product of the base and the power.
• The third law of indices states that when expressions with the same index are divided, the indices
are subtracted.
• The fourth law of indices states that when an expression with a power is raised to another power,
the indices are multiplied.
• The use of indices can help to simplify expressions and make calculations easier, particularly when
dealing with large or complex numbers.
Power Dissipation in a Resistor
• The power, P, dissipated in a resistor is given by the formula P = I^2 * R, where I is the current
flowing through the resistor and R is the resistance value. P is measured in watts, I is measured in
amps, and R is measured in ohms.
• There is an alternative formula for power dissipation in a resistor that uses the voltage, V, across the
resistor. Using Ohm's law, we can derive the formula P = V^2 / R.
• When dividing expressions involving indices, we subtract the indices if the bases are the same.
• Negative indices can be interpreted by inverting the expression and changing the sign of the index.
For example, a^-m = 1/a^m.
• To simplify expressions with negative indices, we can rewrite them using positive indices by
inverting the expression and changing the sign of the index.
• We can use the laws of indices to simplify expressions involving powers of numbers or variables.
Resistors in parallel
• Resistors in parallel are a common arrangement in electrical circuits where two or more resistors
are connected across the same voltage source terminals.
• Figure 1.1 shows two resistors R1 and R2 connected in parallel with a voltage source.
