Shortcut Methods and Tricks for Solving Numericals on Electromotive Force (EMF) and Ohm’s Law

1. Ohm’s Law:

• To find the current (I) flowing through a circuit:

  I = V/R

  where V is the potential difference in volts and R is the resistance in ohms.

• To find the resistance (R) of a conductor:

  R = V/I

  where V is the potential difference in volts and I is the current in amperes.

• To find the voltage (V) required to drive a current (I) through a resistor (R):

  V = I x R

2. Electromotive Force (EMF):

• To find the EMF (E) of a battery:

  E = V + Ir

  where V is the terminal voltage of the battery, I is the current flowing through the circuit, and r is the internal resistance of the battery.

• To find the internal resistance (r) of a battery:

  r = (E - V)/I

  where E is the EMF of the battery, V is the terminal voltage of the battery, and I is the current flowing through the circuit.

• To find the current (I) drawn from a battery:

  I = E/(R + r)

  where E is the EMF of the battery, R is the external resistance connected to the battery, and r is the internal resistance of the battery.

3. Combination of Resistors:

• To find the total resistance (R_total) of resistors connected in series:

  R_total = R_1 + R_2 + ... + R_n

  where R_1, R_2, …, R_n are the resistances of the individual resistors.

• To find the equivalent resistance (R_eq) of resistors connected in parallel:

  1/R_eq = 1/R_1 + 1/R_2 + ... + 1/R_n

  where R_1, R_2, …, R_n are the resistances of the individual resistors.

• To find the total current (I) flowing through a circuit with resistors connected in parallel:

  I = E/(R_eq + r)

  where E is the EMF of the battery, R_eq is the equivalent resistance of the parallel resistors, and r is the internal resistance of the battery.

4. Kirchhoff’s Laws:

• Kirchhoff’s Current Law (KCL) states that the sum of currents flowing into a junction must equal the sum of currents flowing out of that junction.

• Kirchhoff’s Voltage Law (KVL) states that the sum of potential differences around a closed loop in a circuit must equal zero.

To apply Kirchhoff’s laws, you can use the following steps:

• Label the currents and potential differences in the circuit.
• Write KCL equations for each junction.
• Write KVL equations for each loop.
• Solve the equations simultaneously to find the unknown currents and potential differences.

By using these shortcut methods and tricks, you can simplify the process of solving numericals on electromotive force and Ohm’s law, making it easier to find accurate solutions efficiently.